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.
- First, find the area of the base. Since the base is a square, the area \( B \) can be calculated as:
\[ B = \text{side}^2 = 3 , \text{in.} \times 3 , \text{in.} = 9 , \text{in.}^2 \]
- 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 \( 15 , \text{in.}^3 \).