Question

find the volume of a pyramid with a square base, where the side length of the base is 18.5 in and the height of the pyramid is 10.9 in. round your answer to the nearest tenth of a cubic inch.

Explanation:

Step1: Recall the formula for the volume of a square - based pyramid

The volume \(V\) of a pyramid with a square base 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 base \(s = 18.5\) in. Then the area of the base \(B=s^{2}=(18.5)^{2}\) square inches.
\((18.5)^{2}=18.5\times18.5 = 342.25\) square inches.

Step3: Substitute the values of \(B\) and \(h\) into the volume formula

We know that \(h = 10.9\) in and \(B = 342.25\) square inches.
Using the formula \(V=\frac{1}{3}Bh\), we substitute the values:
\(V=\frac{1}{3}\times342.25\times10.9\)

First, calculate \(342.25\times10.9\):
\(342.25\times10.9 = 342.25\times(10 + 0.9)=342.25\times10+342.25\times0.9=3422.5+308.025 = 3730.525\)

Then, divide by 3:
\(V=\frac{3730.525}{3}\approx1243.5083\)

Step4: Round to the nearest tenth

Rounding \(1243.5083\) to the nearest tenth, we look at the hundredth place. The digit in the hundredth place is 0, which is less than 5, so we keep the tenths place digit as it is. So \(V\approx1243.5\) cubic inches.

Answer:

\(1243.5\)