Question

The prism and pyramid above have the same width, length, and height. The volume of the prism is 36 cm3. What is the volume of the pyramid?

Answer 1

The pyramid's formula for Volume is identical to the formula for Volume of a prism, except for having a factor 1/3.

Base Area and height being the same for a pyramid and a prism, the volume of the pyramid is always one third that of the prism.

A similiar fact pertains to Cone vs Cylinder...these 3 dimensional volumes have a ratio of 1/3 to one another.

In two dimensions, there's a ratio of 1/2 between areas of triangles and rectangles having the same base & height.

Answer 2

The volume of the pyramid is 12cm³ ( option D)

The volume of a prism is expressed as ;

V = b × h

where b is the base area and h is the height of the prism.

The volume of a pyramid is expressed as;

V = 1/3 bh

where b is the base area and h is the height of the pyramid.

This means that volume of a pyramid = 1/3 volume of a prism

volume of prism = 36cm³

volume of pyramid = 1/3 × 36

= 12cm³

Therefore the volume of the pyramid is 12cm³