Question

A crystal perfume bottle is in the shape of a square pyramid. The length of one of the sides of the base is 3 in., and the height of the bottle is 5 in. What is the volume of the bottle?(1 point)
in.3

1 answer

The volume \( V \) of a pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

For a square pyramid, the base area \( A \) is given by:

\[ A = \text{side length}^2 \]

In this case, the side length of the base is 3 inches, so:

\[ A = 3 , \text{in} \times 3 , \text{in} = 9 , \text{in}^2 \]

The height \( h \) of the pyramid is 5 inches. Plugging the values into the volume formula:

\[ V = \frac{1}{3} \times 9 , \text{in}^2 \times 5 , \text{in} \]

\[ V = \frac{1}{3} \times 45 , \text{in}^3 \]

\[ V = 15 , \text{in}^3 \]

Therefore, the volume of the bottle is

\[ \boxed{15 , \text{in}^3} \]