Question

find the volume of a right circular cone that has a height of 15.6 cm and a base with a radius of 7.8 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Recall cone volume formula

The volume $V$ of a right circular cone is given by $V = \frac{1}{3}\pi r^2 h$, where $r$ is the base radius and $h$ is the height.

Step2: Substitute given values

Substitute $r = 7.8\ \text{cm}$ and $h = 15.6\ \text{cm}$ into the formula:
$V = \frac{1}{3} \pi (7.8)^2 (15.6)$

Step3: Calculate base area first

Compute $(7.8)^2 = 60.84$, then multiply by $15.6$:
$60.84 \times 15.6 = 949.104$

Step4: Compute final volume

Multiply by $\frac{1}{3}\pi$:
$V = \frac{1}{3} \times 949.104 \times \pi \approx 316.368 \times 3.1416 \approx 993.0$

Answer:

$993.0$ cubic centimeters