7th Grade Math Surface Area And Volume Unit Test

<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 >

<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 >

<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 >

<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 >

<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 >

<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 >

<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 >

<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 >

<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>

<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>

<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>

<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>

<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>

<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>

<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>

<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>

<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>