Geometry: Rectangular Prism and Pyramid Volume

<p>8 $cm^{3}$ (C)</p> Signup and view all the answers

<p>20 $cm^{3}$ (C)</p> Signup and view all the answers

<p>To show that the volume of a pyramid is one-third the volume of a rectangular prism with the same base and height. (B)</p> Signup and view all the answers

<p>To ensure that the pyramid can fit perfectly inside the rectangular prism. (A)</p> Signup and view all the answers

<p>Solve problems involving the volumes of cubes and rectangular prisms. (C)</p> Signup and view all the answers

<p>A 3D geometrical collapsible pyramid and a rectangular prism. (D)</p> Signup and view all the answers

<p>The relationship between the volume of a pyramid and the volume of a rectangular prism. (C)</p> Signup and view all the answers

<p>Square (D)</p> Signup and view all the answers

<p>4 (C)</p> Signup and view all the answers

<p>$rac{1}{3} imes (base area) imes (height)$ (A)</p> Signup and view all the answers

<p>108 cm³ (C)</p> Signup and view all the answers

<p>150 cubic units (A)</p> Signup and view all the answers

<p>$\frac{1}{3} \times$ (base area) $\times$ (height) (D)</p> Signup and view all the answers

<p>The distance from the apex of the pyramid to the midpoint of a side of the base. (A)</p> Signup and view all the answers

<p>1600 $in^3$ (B)</p> Signup and view all the answers

<p>4 cm (D)</p> Signup and view all the answers

<p>4 $in^3$ (D)</p> Signup and view all the answers

The amount of space inside a pyramid, calculated using the formula V = 1/3 * base area * height.

The mathematical expression used to calculate the volume of a pyramid: V = 1/3 * B * h, where B is the base area and h is height.

A pyramid with a square base and four triangular faces meeting at a point above the base.

A three-dimensional shape with six faces, all rectangular, where opposite faces are equal in area.

Studying volumes or patterns through specific examples to discover general principles, such as the relationship between pyramids and prisms.

A pyramid with a square base and apex directly above the center of the base.

Calculated by multiplying the base area by the height: V = base area × height.

Volume of the largest pyramid that fits in a prism equals one-third the prism’s volume: V = (1/3) × prism volume.

A polyhedron with a common vertex called the apex.

The area of the bottom face of a pyramid.

Use the Pythagorean theorem to find vertical height.

For right triangles: a² + b² = c², where c is hypotenuse.

Volume = (1/3) x (base area) x (height) for any pyramid.

Volume = (1/3) x (5 in x 8 in) x (15 in) = 200 in³.

For side 6 cm and height 9 cm, use Volume formula to find the answer.

If a prism shares dimensions with a pyramid, its volume is base area times height (not divided by 3).