Question

lesson 8: surface area and volume square pyramid surface area and volume formulas what is the volume of a square pyramid with a height of 4 cm and a base with a side of 9 cm? a. 36 cubic cm b. 48 cubic cm c. 52 cubic cm d. 108 cubic cm check answer

Explanation:

Step1: Recall volume formula for square pyramid

The volume \( V \) of a square pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Calculate the area of the base

The base is a square with side length \( s = 9\space\text{cm} \). The area of a square is \( B=s^{2} \), so \( B = 9^{2}=81\space\text{cm}^2 \).

Step3: Substitute values into the volume formula

We know \( h = 4\space\text{cm} \) and \( B = 81\space\text{cm}^2 \). Substituting into \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}\times81\times4 \).
First, calculate \( \frac{1}{3}\times81 = 27 \), then \( 27\times4=108 \). So the volume is \( 108\space\text{cubic cm} \).

Answer:

d. 108 cubic cm