Question

find the volume of a pyramid with a square base, where the area of the base is 19.6 cm² and the height of the pyramid is 12.7 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a 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.

Step2: Substitute the given values into the formula

We are given that \( B = 19.6\space cm^{2} \) and \( h=12.7\space cm \). Substituting these values into the formula, we get \( V=\frac{1}{3}\times19.6\times12.7 \).

Step3: Calculate the value

First, calculate \( 19.6\times12.7 = 248.92 \). Then, divide this result by 3: \( V=\frac{248.92}{3}\approx82.9733\space cm^{3} \).

Step4: Round to the nearest tenth

Rounding \( 82.9733 \) to the nearest tenth gives \( 83.0 \) (since the hundredth digit is 7, which is greater than or equal to 5, we round up the tenth digit).

Answer:

\( 83.0\space cm^{3} \)