Question

a solid right pyramid has a square base. the length of the base edge is 4 cm and the height of the pyramid is 3 cm. what is the volume of the pyramid? 12 cm³ 16 cm³ 32 cm³ 48 cm³

Explanation:

Step1: Recall the volume formula for a pyramid

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

Step2: Calculate the area of the square base

The base is a square with edge length \( s = 4\space\text{cm} \). The area of a square is \( B=s^{2} \), so \( B = 4^{2}=16\space\text{cm}^2 \).

Step3: Substitute values into the volume formula

We know \( B = 16\space\text{cm}^2 \) and \( h = 3\space\text{cm} \). Substituting into \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}\times16\times3 \).

Step4: Simplify the expression

\( \frac{1}{3}\times16\times3=16\space\text{cm}^3 \) (the 3 in the numerator and denominator cancels out, leaving \( 16 \)).

Answer:

\( 16\space\text{cm}^3 \) (corresponding to the option "16 \( \text{cm}^3 \)")