Solve For Missing Dimension Given Volume (Word Problems) Problems

<p>Dorothy's Donuts has boxes for customers who buy at least `12` donuts. Each box has a volume of `520` `text{in}^3`. The box is `10` `text{in}` wide and `4` `text{in}` tall. </p><p>What is the length `(L)` of the box?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p></p><RectangularPrism3D data-props='{ "rectangle_base": 13, "prism_height": 4, "prism_length": 10, "height_oriantation_right": true, "rotate_y_axis": 0.1, "rotate_x_axis": 0, "interactive": false, "faces": [ { "id": 1, "position": "front", "color": "orange", "opacity": 0 }, { "id": 2, "position": "back", "opacity": 0, "color": "orange" }, { "id": 3, "position": "left", "opacity": 0, "color": "blue" }, { "id": 4, "position": "right", "opacity": 0, "color": "blue" }, { "id": 6, "position": "top", "opacity": 0, "color": "blue" }, { "id": 5, "position": "bottom", "color": "blue", "opacity": 0 } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "#080808", "label": "" }, { "id": 2, "face": "front", "position": "right", "color": "#080808", "label": " " }, { "id": 3, "face": "front", "position": "bottom", "color": "#080808", "label": "L" }, { "id": 4, "face": "front", "position": "top", "color": "#080808", "label": " " }, { "id": 5, "face": "back", "position": "left", "color": "#080808", "label": " " }, { "id": 6, "face": "back", "position": "right", "color": "#080808", "label": "4 in" }, { "id": 7, "face": "back", "position": "bottom", "color": "#080808", "label": " " }, { "id": 8, "face": "back", "position": "top", "color": "#080808", "label": " " }, { "id": 9, "face": "right", "position": "top", "color": "#080808", "label": " " }, { "id": 10, "face": "right", "position": "bottom", "color": "#080808", "label": "10 in" }, { "id": 11, "face": "left", "position": "bottom", "color": "black", "label": " " }, { "id": 12, "face": "left", "position": "top", "color": "black", "label": " " } ], "unit": "in", "show_default_labels": false, "animation_delay": 0, "animation_duration": 0, "animation_sequences": [], "show_animation": false, "length_offset_y": 0, "height_offset_y": 0.3, "zoom": 2}'></RectangularPrism3D>

<p>Theo is looking for a case to store his moviemaking equipment. One case he likes has a volume of `1text{,}827` `text{in}^3`. The length of the case is `18` `text{in}` and it has a height of `7` `text{in}`. </p><p>What is the width of the case?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p> </p>

<p>Sam is filling a small rectangular pool with water for his little sister to wade in. The volume of the pool is `7` `text{ft}^3`. The pool has a length of `4` `text{ft}` and a width of `3.5` `text{ft}`. </p><p>What is the height of the pool?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p></p>

<p>After watching a spy movie, Annabelle figured out how to create a special secret compartment in the heel of one of her shoes. The compartment has a volume of `18` `text{cm}^3`. It is `4` `text{cm}` long and `3` `text{cm}` wide. </p><p>What is the height of the compartment?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p></p>

<p>Joey used a long box to make a tunnel for his little brother's toy cars. The volume of the box is `1.8` `text{m}^3`. The width of the box is `0.12` `text{m}` and the height is `0.15` `text{m}`. </p><p>What is the length of the box?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p><p/>

<p>Oliver buys a new aquarium for his pet octopus. The aquarium holds `5 5/8` `text{ft}^3` of water. The length is `3` `text{ft}` and the width is `1 1/4` `text{ft}`. </p><p>What is the height of the aquarium?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p> </p>

<p>Amarra is playing with her sandcastle toys at the beach. She has a rectangular plastic box that is `3 1/2` `text{in}` long and `1 1/2` `text{in}` wide. The box can hold `13 1/8` `text{in}^3` of sand. </p><p>What is the height of the plastic box?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p></p>