Question

review homework: unit 3 - geometry question 35, 6.5.11 hw score: 56.9%, 33 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 (a square pyramid)

The base is a square with side length \( s = 3 \, \text{cm} \), and the height \( h = 12 \, \text{cm} \). The formula for the volume \( V \) of a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base.

Step2: Calculate the base area \( B \)

For a square base, \( B = s^2 \). Substituting \( s = 3 \), we get \( B = 3^2 = 9 \, \text{cm}^2 \).

Step3: Calculate the volume \( V \)

Using the pyramid volume formula \( V=\frac{1}{3}Bh \), substitute \( B = 9 \) and \( h = 12 \):
\( V=\frac{1}{3}\times9\times12 \)
First, \( \frac{1}{3}\times9 = 3 \), then \( 3\times12 = 36 \).

Answer:

\( 36 \, \text{cubic centimeters} \) (or \( 36 \, \text{cm}^3 \))