Question

what is the volume of this cone?
round your answer to the nearest hundredth.
13 cm
12 cm
cubic centimeters

Explanation:

Step1: Find radius of base

Radius $r = \frac{12}{2} = 6$ cm

Step2: Calculate height using Pythagoras

Height $h = \sqrt{13^2 - 6^2} = \sqrt{169 - 36} = \sqrt{133} \approx 11.5326$ cm

Step3: Compute volume of cone

Volume $V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (6)^2 (11.5326) \approx \frac{1}{3}\pi \times 36 \times 11.5326 \approx 12\pi \times 11.5326 \approx 434.67$

Answer:

434.67 cubic centimeters