Question

the volume of this cone is 23.864 cubic centimeters. what is the radius of this cone?
round your answer to the nearest hundredth.
5.7 cm
r ≈ centimeters

Explanation:

Step1: Identify cone volume formula

Volume formula: $V = \frac{1}{3}\pi r^2 h$
Given: $V=23.864$, $h=5.7$, $\pi\approx3.14$

Step2: Rearrange for $r^2$

$r^2 = \frac{3V}{\pi h}$
Substitute values: $r^2 = \frac{3\times23.864}{3.14\times5.7}$

Step3: Calculate $r^2$

Numerator: $3\times23.864=71.592$
Denominator: $3.14\times5.7\approx17.898$
$r^2\approx\frac{71.592}{17.898}\approx4.00$

Step4: Find $r$

$r\approx\sqrt{4.00}=2.00$

Answer:

2.00 centimeters