Question

use the diagram to answer the question
a cone has a radius of 10 cm and a height of 22 cm. what is the volume of the cone? (round to the nearest whole number if necessary)
230 cm³
460 cm³
2,303 cm³
6,906 cm³

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 10\space cm\) and \(h=22\space cm\). Substitute into the formula: \(V=\frac{1}{3}\times\pi\times(10)^{2}\times22\).
First, calculate \((10)^{2}=100\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times100\times22=\frac{2200\pi}{3}\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(V=\frac{2200\times3.14}{3}=\frac{6908}{3}\approx2302.67\). Rounding to the nearest whole number gives \(V\approx2303\space cm^{3}\).

Answer:

C. \(2303\space cm^{3}\)