Question

find the volume of a pyramid with a square base, where the area of the base is 19.8 cm² and the height of the pyramid is 13.9 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Recall pyramid volume formula

The volume $V$ of a pyramid is given by $V = \frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height.

Step2: Substitute given values

Substitute $B = 19.8\ \text{cm}^2$ and $h = 13.9\ \text{cm}$ into the formula:
$V = \frac{1}{3} \times 19.8 \times 13.9$

Step3: Calculate intermediate product

First compute $19.8 \times 13.9 = 275.22$

Step4: Compute final volume

$V = \frac{275.22}{3} = 91.74$

Step5: Round to nearest tenth

Round $91.74$ to one decimal place: $91.7$

Answer:

$91.7$ cubic centimeters