Question

Given that these 2 prisms have the same height of 6 in, do they have the same volume, too? What is the volume?

cavalieri 2

A. Yes, 960 in³
B. No, not the same volume
C. Yes, 480 in³
D. No, not enough information

Answer 1

The volume of a rectangular prism is:

l * w * h

Plug the values in:

4 * 20 * 6 = 480 inches cubed

The volume of a triangular prism is:

B * h

Plug the values in:

(16 * 10)/2 * 6 = 480 inches cubed

So, the answer is (C).

Answer 2

The volume of a prism is given by the product of its base area and its height. Since the two heights are the same, let's look at the bases.

The first prism has a rectangle for base, with sides 4 and 20 inches. This means that its area is $4\cdot 20 = 80$ squared inches.

The second prism has a right triangle for base, with legs 16 and 10 inches. This means that its area is

$\cfrac{16\cdot 10}{2} = \cfrac{160}{2} = 80$ squared inches.

So, both prisms have the same height and the same base area. This means that they have the same volume as well, since in both cases it is given by

$V = \text{base area} \times \text{height} = 80 \cdot 6 = 480$ inches cubed.