Question

an architect designed an attic space in the shape of a square - pyramid. after reviewing the design, he decided to make a second design for an attic space in the shape of an oblique pyramid. he created models of both designs as shown. both models were cut horizontally at the same height, finding the cross - sections to have the same area. several other horizontal cross - sections were analyzed and found to have the same area as well. both pyramid models also have the same height, a. which formula would allow the architect to calculate the volume of his second attic space design? a. v = (\frac{1}{3}s^{2}a) b. v = (\frac{1}{3}s^{2}c) c. v = (s^{2}a) d. v = (\frac{1}{2}s^{2}h)

Explanation:

Step1: Recall volume formula for pyramid

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height. In the second design, if the base of the square - pyramid has side length $s$ and the height is $a$, the base - area $B = s^{2}$.

Step2: Substitute into volume formula

Substituting $B = s^{2}$ and $h=a$ into the volume formula $V=\frac{1}{3}Bh$, we get $V=\frac{1}{3}s^{2}a$.

Answer:

A. $V=\frac{1}{3}s^{2}a$