Question

find the volume of a pyramid with a square base, where the side length of the base is 4.6 m and the height of the pyramid is 7.2 m. round your answer to the nearest tenth of a cubic meter.

Explanation:

Step1: Recall the volume formula for 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 square base \(s = 4.6\space m\). Then the area of the base \(B=s^{2}=(4.6)^{2}\space m^{2}\).
\((4.6)^{2}=4.6\times4.6 = 21.16\space m^{2}\)

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

We know that \(h = 7.2\space m\) and \(B = 21.16\space m^{2}\). Substituting these values into \(V=\frac{1}{3}Bh\), we get:
\(V=\frac{1}{3}\times21.16\times7.2\)

First, calculate \(21.16\times7.2\):
\(21.16\times7.2=(20 + 1.16)\times7.2=20\times7.2+1.16\times7.2 = 144+8.352 = 152.352\)

Then, calculate \(\frac{1}{3}\times152.352\):
\(\frac{1}{3}\times152.352 = 50.784\)

Step4: Round to the nearest tenth

To round \(50.784\) to the nearest tenth, we look at the hundredth place. The digit in the hundredth place is \(8\), which is greater than or equal to \(5\). So we round up the digit in the tenth place.
\(50.784\approx50.8\) (rounded to the nearest tenth)

Answer:

\(50.8\) cubic meters