Question

Volume of Pyramids Practice
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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

Answer 1

To find the volume of a square pyramid, you can use the formula:

\[
V = \frac{1}{3} \times B \times h
\]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid.

1. First, find the area of the base. Since the base is a square, the area \( B \) can be calculated as:

\[
B = \text{side}^2 = 3 \, \text{in.} \times 3 \, \text{in.} = 9 \, \text{in.}^2
\]

2. Now, plug the values into the volume formula. The height \( h \) is given as 5 in.

\[
V = \frac{1}{3} \times 9 \, \text{in.}^2 \times 5 \, \text{in.}
\]
\[
V = \frac{1}{3} \times 45 \, \text{in.}^3
\]
\[
V = 15 \, \text{in.}^3
\]

Therefore, the volume of the crystal perfume bottle is \( 15 \, \text{in.}^3 \).