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 answer

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. Calculate the area of the base (B): The base of the pyramid is a square, so the area \( B \) is given by:

\[ B = \text{side}^2 \]

Given that the length of one side of the base is 3 inches:

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

  1. Use the height (h): The height of the pyramid is given as 5 inches:

\[ h = 5 , \text{in} \]

  1. Calculate the volume (V): Now, plug in the values into the volume formula:

\[ V = \frac{1}{3} \times 9 \times 5 \]

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

Therefore, the volume of the bottle is

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