# 7th Grade Math Surface Area And Volume Unit Test

17 questions

### #1 of 17:Mild

Surface Area and Volume

<p>What is the surface area of the prism below?</p><TriangularPrism3D data-props='{ "triangle_base": 6, "triangle_left_side": 6, "triangle_right_side": 6, "prism_height": 5, "prism_length": 8, "triangle_type": "triangular_prism", "faces": [ { "id": 1, "position": "front", "color": "#D6D6D6" }, { "id": 2, "position": "back", "color": "#F8F8F8" }, { "id": 3, "position": "bottom", "color": "#F8F8F8" }, { "id": 4, "position": "left", "color": "#F8F8F8" }, { "id": 5, "position": "right", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 7, "face": "right", "position": "top", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 8, "face": "right", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 9, "face": "left", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "12 yd", "color": "black" }, "unit": "in", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></TriangularPrism3D >

### #2 of 17:Medium

Surface Area and Volume

<p>What is the surface area of the prism below?</p><TriangularPrism3D data-props='{ "triangle_base": 13, "triangle_left_side": 17, "triangle_right_side": 17, "prism_height": 16, "prism_length": 21, "triangle_type": "triangular_prism", "faces": [ { "id": 1, "position": "front", "color": "#D6D6D6" }, { "id": 2, "position": "back", "color": "#F8F8F8" }, { "id": 3, "position": "bottom", "color": "#F8F8F8" }, { "id": 4, "position": "left", "color": "#F8F8F8" }, { "id": 5, "position": "right", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 7, "face": "right", "position": "top", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 8, "face": "right", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 9, "face": "left", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "12 yd", "color": "black" }, "unit": "m", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></TriangularPrism3D >

### #3 of 17:Medium

Surface Area and Volume

<p>What is the surface area of the prism below?</p><TriangularPrism3D data-props='{ "triangle_base": 7, "triangle_left_side": 10, "triangle_right_side": 10, "prism_height": 9, "prism_length": 16, "triangle_type": "triangular_prism", "faces": [ { "id": 1, "position": "front", "color": "#D6D6D6" }, { "id": 2, "position": "back", "color": "#F8F8F8" }, { "id": 3, "position": "bottom", "color": "#F8F8F8" }, { "id": 4, "position": "left", "color": "#F8F8F8" }, { "id": 5, "position": "right", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 7, "face": "right", "position": "top", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 8, "face": "right", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } }, { "id": 9, "face": "left", "position": "bottom", "color": "#080808", "label": { "text": "5yd", "show_label": true } } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "12 yd", "color": "black" }, "unit": "in", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></TriangularPrism3D >

### #4 of 17:Medium

Surface Area and Volume

<p>What is the volume of the prism below?</p><TriangularPrism3D data-props='{ "triangle_base": 15, "triangle_left_side": 12, "triangle_right_side": 12, "prism_height": 9.5, "prism_length": 16, "triangle_type": "triangular_prism", "faces": [ { "id": 1, "position": "front", "color": "#D6D6D6" }, { "id": 2, "position": "back", "color": "#F8F8F8" }, { "id": 3, "position": "bottom", "color": "#F8F8F8" }, { "id": 4, "position": "left", "color": "#F8F8F8" }, { "id": 5, "position": "right", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": { "text": "14 cm", "show_label": true } }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 7, "face": "right", "position": "top", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 8, "face": "right", "position": "bottom", "color": "#080808", "label": { "text": "16 cm", "show_label": true } }, { "id": 9, "face": "left", "position": "bottom", "color": "#080808", "label": { "text": " ", "show_label": true } } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "9.5 cm", "color": "black" }, "unit": "cm", "show_default_labels": false, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></TriangularPrism3D >

### #5 of 17:Medium

Surface Area and Volume

<p>What is the volume of the prism below?</p><TriangularPrism3D data-props='{ "triangle_base": 22, "triangle_left_side": 12, "triangle_right_side": 13, "prism_height": 6.2, "prism_length": 22, "triangle_type": "triangular_prism", "faces": [ { "id": 1, "position": "front", "color": "#D6D6D6" }, { "id": 2, "position": "back", "color": "#F8F8F8" }, { "id": 3, "position": "bottom", "color": "#F8F8F8" }, { "id": 4, "position": "left", "color": "#F8F8F8" }, { "id": 5, "position": "right", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": { "text": "22 cm", "show_label": true } }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 7, "face": "right", "position": "top", "color": "#080808", "label": { "text": " ", "show_label": true } }, { "id": 8, "face": "right", "position": "bottom", "color": "#080808", "label": { "text": "22 cm", "show_label": true } }, { "id": 9, "face": "left", "position": "bottom", "color": "#080808", "label": { "text": " ", "show_label": true } } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "6.5 cm", "color": "black" }, "unit": "cm", "show_default_labels": false, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></TriangularPrism3D >

### #6 of 17:Mild

Surface Area and Volume

<p>Identify the cross-section of the 3D figure.</p><CrossSection3D data-props='{ "plane": "horizontal", "shape": "rectangular_prism", "opacity": 1, "plane_color": "#42D540", "shape_color": "#D8D8DF", "cross_section_color": "#028500"}'></CrossSection3D >

### #7 of 17:Medium

Surface Area and Volume

<p>Identify the cross-section of the 3D figure.</p><CrossSection3D data-props='{ "plane": "horizontal", "shape": "square_pyramid", "opacity": 1, "plane_color": "#42D540", "shape_color": "#D8D8DF", "cross_section_color": "#028500"}'></CrossSection3D >

### #8 of 17:Spicy

Surface Area and Volume

<p>Identify the cross-section of the 3D figure.</p><CrossSection3D data-props='{ "plane": "vertical", "shape": "cylinder", "opacity": 1, "plane_color": "#03C700", "shape_color": "D8D8DF", "cross_section_color": "#028500"}'></CrossSection3D >

### #9 of 17:Mild

Surface Area and Volume

<p>A square pyramid has a side length of `4` yards on the base and a slant height of `9` yards?</p><SquarePyramid3D data-props='{ "triangle_base": 4, "pyramid_height": 9, "faces": [ { "id": 1, "position": "front", "color": "#F8F8F8" }, { "id": 2, "position": "left", "color": "#F8F8F8" }, { "id": 3, "position": "back", "color": "#F8F8F8" }, { "id": 4, "position": "right", "color": "#F8F8F8" }, { "id": 5, "position": "bottom", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 7, "face": "right", "position": "bottom", "color": "#080808", "label": "5yd" }, { "id": 8, "face": "left", "position": "bottom", "color": "#080808", "label": "5yd" } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "9 yd", "color": "black" }, "unit": "yd", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></SquarePyramid3D ><p>What is the surface area of the square pyramid?</p>

### #10 of 17:Medium

Surface Area and Volume

<p>A square pyramid has a side length of `7` inches on the base and a slant height of `11` inches?</p><SquarePyramid3D data-props='{ "triangle_base": 7, "pyramid_height": 11, "faces": [ { "id": 1, "position": "front", "color": "#F8F8F8" }, { "id": 2, "position": "left", "color": "#F8F8F8" }, { "id": 3, "position": "back", "color": "#F8F8F8" }, { "id": 4, "position": "right", "color": "#F8F8F8" }, { "id": 5, "position": "bottom", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 7, "face": "right", "position": "bottom", "color": "#080808", "label": "5yd" }, { "id": 8, "face": "left", "position": "bottom", "color": "#080808", "label": "5yd" } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "11 in", "color": "black" }, "unit": "in", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></SquarePyramid3D ><p>What is the surface area of the square pyramid?</p>

### #11 of 17:Medium

Surface Area and Volume

<p>A square pyramid has a side length of `17` meters on the base and a slant height of `13` meters?</p><SquarePyramid3D data-props='{ "triangle_base": 17, "pyramid_height": 13, "faces": [ { "id": 1, "position": "front", "color": "#F8F8F8" }, { "id": 2, "position": "left", "color": "#F8F8F8" }, { "id": 3, "position": "back", "color": "#F8F8F8" }, { "id": 4, "position": "right", "color": "#F8F8F8" }, { "id": 5, "position": "bottom", "color": "#F8F8F8" } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 4, "face": "back", "position": "left", "color": "#080808", "label": "5 yd" }, { "id": 5, "face": "back", "position": "right", "color": "#080808", "label": "5 yd" }, { "id": 6, "face": "back", "position": "bottom", "color": "#080808", "label": "5 yd" }, { "id": 7, "face": "right", "position": "bottom", "color": "#080808", "label": "5yd" }, { "id": 8, "face": "left", "position": "bottom", "color": "#080808", "label": "5yd" } ], "face_altitude": { "show_altitude": true, "show_angle": true, "label": "13 m", "color": "black" }, "unit": "m", "show_default_labels": true, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false}'></SquarePyramid3D ><p>What is the surface area of the square pyramid?</p>

### #12 of 17:Mild

Surface Area and Volume

<p>The composite figure below is made up of two semicircles.</p><CompositeSemiCircle data-props='{ "base_circle": { "radius": { "value": 5, "label": { "text": " 5 cm", "color": "black", "show": false, "background": "none" } }, "diameter": { "value": 10, "label": { "text": "10 cm", "color": "black", "show": true, "background": "none" }, "color": "black", "line_style": "dashed" }, "show_center": true, "color": "black", "border_color": "black" }, "orientation": 180, "adjacent_circles": [ { "radius": { "value": 2, "label": { "text": "2 cm ", "color": "black", "show": false, "background": "none" }, "color": "black", "line_style": "dashed", "show_radius": false }, "diameter": { "value": 4, "label": { "text": "4 cm", "color": "black", "show": true, "background": "none" }, "color": "black" }, "show_center": true, "color": "black", "border_color": "black", "offset": -4 } ], "debug": false}'></CompositeSemiCircle ><p>What is the area of the given composite figure?</br><highlight data-color="#666" data-style="italic">Round your answer to the nearest hundredth.</highlight></p>

### #13 of 17:Spicy

Surface Area and Volume

<p>The composite figure below is made up of three semicircles.</p><CompositeSemiCircle data-props='{ "base_circle": { "radius": { "value": 12, "label": { "text": "12 cm", "show": true, "background": "none" } }, "diameter": { "value": 24, "label": { "text": "24 cm", "show": false, "background": "none" }, "line_style": "simple" }, "show_center": true, "color": "black" }, "orientation": 90, "adjacent_circles": [ { "radius": { "value": 6, "label": { "text": "6 cm", "show": true, "background": "none" }, "color": "black", "line_style": "dashed", "show_radius": false }, "diameter": { "value": 12, "label": { "text": "12 cm", "show": true, "background": "none" } }, "show_center": true, "color": "black", "offset": -6 }, { "radius": { "value": 6, "label": { "text": "6 cm", "show": false, "background": "none" }, "color": "black", "line_style": "dashed", "show_radius": false }, "diameter": { "value": 12, "label": { "text": "12 cm", "show": true, "background": "none" } }, "show_center": true, "color": "black", "offset": 6 } ], "debug": false}'></CompositeSemiCircle ><p> What is the area of the given composite figure?<br><highlight data-color="#666" data-style="italic">Round your answer to the nearest hundredth.</highlight> </p>

### #14 of 17:Medium

Surface Area and Volume

<p>The composite figure below is made up of two semicircles.</p><CompositeSemiCircle data-props='{ "base_circle": { "radius": { "value": 8, "label": { "text": "17 cm", "show": false, "background": "none" } }, "diameter": { "value": 16, "label": { "text": "34 cm", "show": false, "background": "none" }, "line_style": "dashed" }, "show_center": true, "color": "black" }, "orientation": 0, "adjacent_circles": [ { "radius": { "value": 4, "label": { "text": "8.5 cm", "show": false, "background": "none" }, "color": "black", "line_style": "dashed", "show_radius": false }, "diameter": { "value": 8, "label": { "text": "17 cm", "show": true, "background": "black" } }, "show_center": true, "color": "#D8D8DF", "offset": -4 } ], "debug": false, "scale_factor": 2}'></CompositeSemiCircle ><p>What is the area of the given composite figure?<br><highlight data-color="#666" data-style="italic">Round your answer to the nearest hundredth.</highlight> </p>

### #15 of 17:Mild

Surface Area and Volume

<p>The diagram below shows a triangle inside of a triangle.</p><CompositeShapeInShape data-props='{ "inner": { "type": "triangle", "shape": { "type": "isosceles", "base": { "value": 72, "label": { "text": "8 in" } }, "height": { "value": 45, "label": { "text": "5 in", "background": "none" }, "color": "black" }, "show_right_angle": true, "color": "#FFFFFF", "border_color": "#080808" }, "offset_y": 0, "offset_x": 0 }, "outer": { "type": "triangle", "shape": { "type": "right", "base": { "value": 198, "label": { "text": "22 in" } }, "height": { "value": 153, "label": { "text": "17 in", "background": "white" }, "color": "black" }, "show_right_angle": true, "color": " #D8D8DF", "border_color": "#080808" } }}'></CompositeShapeInShape ><p>What is the area of the shaded region?</p>

### #16 of 17:Medium

Surface Area and Volume

<p>The diagram below shows a rectangle inside of a circle. </p><CompositeShapeInShape data-props='{ "inner": { "type": "rectangle", "shape": { "height": { "value": 60, "label": { "text": "3 mm" }, "side": "left", "color": "black", "highlight": true }, "width": { "value": 100, "label": { "text": "5 mm" }, "color": "black", "side": "top", "highlight": true }, "color": "white", "border_color": "black" }, "offset_y": -75 }, "outer": { "type": "circle", "shape": { "radius": { "value": 180, "label": { "text": "9 mm", "show": true }, "color": "black", "angle": 0 }, "show_center": true, "color": "#D8D8DF", "border_color": "black" } }}'></CompositeShapeInShape ><p>What is the area of the shaded region?<br><highlight data-color="#666" data-style="italic">Use `3.14` for 𝛑</highlight></p>

### #17 of 17:Spicy

Surface Area and Volume

<p>The diagram below shows a circle inside of a triangle. <p><CompositeShapeInShape data-props='{ "inner": { "type": "circle", "shape": { "radius": { "value": 45, "label": { "text": "3 cm", "background": "none", "show": true }, "color": "#080808", "angle": 30 }, "show_center": true, "color": "#FFFFFF", "border_color": "black" }, "offset_x":-5 }, "outer": { "type": "triangle", "shape": { "type": "right", "base": { "value": 180, "label": { "text": "12 cm" }, "color": "black" }, "height": { "value": 210, "label": { "text": "14 cm" }, "color": "black" }, "show_right_angle": true, "color": "#D8D8DF", "border_color": "#000" } }}'></CompositeShapeInShape ><p>What is the area of the shaded region?<br><highlight data-color="#666" data-style="italic">Use `3.14` for 𝛑</highlight></p>

Surface area and volume generally apply to 3-dimensional shapes. The surface area of the object is the exposed area that is occupied by it and the volume is the space occupied by all dimensions of the same. Your students should also take the surface area and volume unit test to improve...

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Surface Area And Volume

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### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”