Find Missing Dimension Of A Rectangular Prism Given Volume Problems

<p>The rectangular prism has a base area of `18` `text{ft}^2` and a volume of `180` `text{ft}^3`.</p><p>What is the height `(h` `text{ft})` of the rectangular prism?</p><RectangularPrism3D data-props='{ "rectangle_base": 3, "prism_height": 10, "prism_length": 6, "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": "gray", "opacity": 0.2 } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "black", "label": "" }, { "id": 2, "face": "front", "position": "right", "color": "black", "label": " " }, { "id": 3, "face": "front", "position": "bottom", "color": "black", "label": "" }, { "id": 4, "face": "front", "position": "top", "color": "black", "label": " " }, { "id": 5, "face": "back", "position": "left", "color": "black", "label": " " }, { "id": 6, "face": "back", "position": "right", "color": "black", "label": "h" }, { "id": 7, "face": "back", "position": "bottom", "color": "black", "label": " " }, { "id": 8, "face": "back", "position": "top", "color": "black", "label": " " }, { "id": 9, "face": "right", "position": "top", "color": "black", "label": " " }, { "id": 10, "face": "right", "position": "bottom", "color": "black", "label": "" }, { "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, "zoom": 7, "horizontal_oriantation": -0.3, "height_offset_y": 0.1, "base_offset_y": 0, "base_offset_x": -0.5, "length_offset_x": -0.2, "rotate_z_axis": 0}'></RectangularPrism3D>

<p>The rectangular prism has a base area of `16` `text{mm}^2` and a volume of `136` `text{mm}^3`.</p><p>What is the height `(h` `text{mm})` of the rectangular prism?</p><RectangularPrism3D data-props='{ "rectangle_base": 4, "prism_height": 8.5, "prism_length": 4, "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": "gray", "opacity": 0.2 } ], "edges": [ { "id": 1, "face": "front", "position": "left", "color": "black", "label": "" }, { "id": 2, "face": "front", "position": "right", "color": "black", "label": " " }, { "id": 3, "face": "front", "position": "bottom", "color": "black", "label": "" }, { "id": 4, "face": "front", "position": "top", "color": "black", "label": " " }, { "id": 5, "face": "back", "position": "left", "color": "black", "label": " " }, { "id": 6, "face": "back", "position": "right", "color": "black", "label": "h" }, { "id": 7, "face": "back", "position": "bottom", "color": "black", "label": " " }, { "id": 8, "face": "back", "position": "top", "color": "black", "label": " " }, { "id": 9, "face": "right", "position": "top", "color": "black", "label": " " }, { "id": 10, "face": "right", "position": "bottom", "color": "black", "label": "" }, { "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, "zoom": 10, "horizontal_oriantation": -0.3, "height_offset_y": 0.1, "base_offset_y": 0, "base_offset_x": -0.5, "length_offset_x": -0.2, "rotate_z_axis": 0}'></RectangularPrism3D>

<p>A rectangular prism has a height of `6` `text{cm}`, a width of `2.5` `text{cm}`, and a volume of `105` `text{cm}^3`.</p><p>What is the length of the rectangular prism?</p>

<p>The rectangular prism has a volume of `130` `text{m}^3`.</p> <p>What is the width `(w` `text{m})` of the rectangular prism?</p><RectangularPrism3D data-props='{ "rectangle_base": 4, "prism_height": 6.5, "prism_length": 5, "height_oriantation_right": true, "rotate_y_axis": 0, "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": "4 m" }, { "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": "6.5 m" }, { "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": "w" }, { "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, "height_offset_x": 0, "height_offset_y": 0.9, "base_offset_x": -0.2, "zoom": 1.5, "vertical_oriantation": 0.3, "horizontal_oriantation": -1, "length_offset_x": 0, "length_offset_y": 0, "base_offset_y": -0.1}'></RectangularPrism3D>

<p>A rectangular prism has a length of `4.5` `text{mm}`, a width of `4` `text{mm}`, and a volume of `90` `text{mm}^3`.</p><p>What is the height of the rectangular prism?</p>

<p>A rectangular prism has a height of `2` `text{m}`, a width of `4/5` `text{m}`, and a volume of `4 4/15` `text{m}^3`.</p><p>What is the length of the rectangular prism?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p>

<p>A rectangular prism has a length of `2 2/3` `text{m}`, a width of `1 1/4` `text{m}`, and a volume of `2 6/7` `text{m}^3`.</p><p>What is the height of the rectangular prism?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p>

<p>The rectangular prism has a volume of `15/4` `text{in}^3`.</p><p>What is the width `(w` `text{in})` of the rectangular prism?</br><highlight data-color="#666" data-style="italic">Write your answer as a whole number, simplified fraction, or exact decimal.</highlight></p><RectangularPrism3D data-props='{ "rectangle_base": 2.5, "prism_height": 0.66, "prism_length": 2.25, "height_oriantation_right": true, "rotate_y_axis": 0, "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": "2 1/2 in" }, { "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": "2/3 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": "w" }, { "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, "height_offset_x": 0.5, "height_offset_y": 0.3, "base_offset_x": -0.2, "zoom": 0, "vertical_oriantation": 0.5, "horizontal_oriantation": -1, "length_offset_x": 0, "length_offset_y": 0, "base_offset_y": -0.3}'></RectangularPrism3D>