Question

a small solid pyramid was installed on top of a monument. the square base of the pyramid is 13.1 centimeters on a side, and the height of the pyramid is 22.2 centimeters. the pyramid has a mass of 5.05 kilograms.
part 1 out of 3
find the volume of the pyramid. round to the nearest hundredth.
the small solid pyramid has a volume of approximately \boxed{} cubic centimeters.

Explanation:

Step1: Recall pyramid volume formula

The volume \( V \) of a square - based pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. For a square base with side length \( s \), the area of the base \( B = s^{2}\).

Step2: Calculate the area of the base

Given that the side length of the square base \( s = 13.1\) centimeters. Then the area of the base \( B=s^{2}=(13.1)^{2}=171.61\) square centimeters.

Step3: Substitute values into the volume formula

We know that \( h = 22.2\) centimeters and \( B = 171.61\) square centimeters. Substitute these values into the formula \( V=\frac{1}{3}Bh\):
\( V=\frac{1}{3}\times171.61\times22.2\)
First, calculate \( 171.61\times22.2 = 171.61\times(22 + 0.2)=171.61\times22+171.61\times0.2=3775.42+34.322 = 3809.742\)
Then, \( V=\frac{3809.742}{3}=1269.914\approx1269.91\) (rounded to the nearest hundredth)

Answer:

\(1269.91\)