Question

find the volume of the solid.
the volume is \\( \square \\) . (simplify your answer.)
(image of a pyramid with base sides 2 cm, 2 cm and height 3 cm)

Explanation:

Step1: Identify the formula for the volume of a pyramid

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

Step2: Calculate the area of the base

The base of the pyramid is a square with side length \( s = 2 \, \text{cm} \). The area of a square is \( B = s^2 \), so \( B = 2^2 = 4 \, \text{cm}^2 \).

Step3: Substitute the values into the volume formula

We know the height \( h = 3 \, \text{cm} \) and the base area \( B = 4 \, \text{cm}^2 \). Substituting these into the formula \( V = \frac{1}{3}Bh \), we get \( V = \frac{1}{3} \times 4 \times 3 \).

Step4: Simplify the expression

Simplifying \( \frac{1}{3} \times 4 \times 3 \), the 3 in the numerator and denominator cancels out, leaving \( V = 4 \, \text{cm}^3 \).

Answer:

\( 4 \) cubic centimeters (or \( 4 \, \text{cm}^3 \))