Question

the oblique pyramid has a square base with an edge length of 5 cm. the height of the pyramid is 7 cm. what is the volume of the pyramid? \\( 11\frac{2}{3}\text{ cm}^3 \\) \\( 43\frac{3}{4}\text{ cm}^3 \\) \\( 58\frac{1}{3}\text{ cm}^3 \\) \\( 87\frac{1}{2}\text{ cm}^3 \\)

Explanation:

Step1: Find the area of the square base

The formula for the area of a square is \( A = s^2 \), where \( s \) is the side length. Here, \( s = 5 \) cm. So, \( A = 5^2 = 25 \) \( \text{cm}^2 \).

Step2: Use 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. We know \( B = 25 \) \( \text{cm}^2 \) and \( h = 7 \) cm. Substituting these values, we get \( V=\frac{1}{3}\times25\times7 \).

Step3: Calculate the volume

\( \frac{1}{3}\times25\times7=\frac{175}{3}=58\frac{1}{3} \) \( \text{cm}^3 \).

Answer:

\( 58\frac{1}{3}\text{ cm}^3 \) (corresponding to the option \( 58\frac{1}{3}\text{ cm}^3 \))