Question

unit 3 - geometry
question 35, 6.5.11
hw score: 75.86%, 44 of 58 points
points: 0 of 1
find the volume of the solid.
the volume is \boxed{} (simplify your answer.)

Explanation:

Step1: Identify the solid and formula

The solid is a square pyramid. The formula for the volume \( V \) of a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.
The base is a square with side length \( s = 5\space\text{cm}\), so the area of the base \( B=s^2=5^2 = 25\space\text{cm}^2\). The height \( h = 9\space\text{cm}\).

Step2: Substitute values into the formula

Substitute \( B = 25\) and \( h=9\) into the volume formula:
\( V=\frac{1}{3}\times25\times9 \)

Step3: Simplify the expression

First, calculate \( 25\times9 = 225 \), then \( \frac{1}{3}\times225=75 \).

Answer:

\( 75\space\text{cubic centimeters} \) (or \( 75\space\text{cm}^3 \))