Question 80·Medium·Math

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A right circular cone has a radius of $6$ centimeters and a height of $8$ centimeters. What is the volume, in cubic centimeters, of the cone?

For cone volume questions, immediately recall and write down $V = \tfrac{1}{3}\pi r^2 h$ , then carefully identify which given number is the radius (and whether any diameter needs to be halved) and which is the height. Plug in the values, square the radius first, multiply by the height, and apply the $\tfrac{1}{3}$ factor last so you do not accidentally forget or double-count it. Finally, match your simplified result to the closest answer choice, usually expressed as a multiple of $\pi$ .

Hints

Click me!

Recall the right formula

Think about the formula for the volume of a cone. How is it related to the volume of a cylinder with the same base and height?

Pick out the radius and height

Identify which number in the problem is the radius and which is the height, and make sure you are not treating the height as a diameter.

Substitute carefully and simplify in stages

After writing the formula with $r$ and $h$ , plug in the values from the problem, square the radius first, then multiply by the height, and only then apply the factor of $\tfrac{1}{3}$ .

Desmos Guide

Compute the cone volume expression

In Desmos, type the expression (1/3)*pi*6^2*8 and press Enter. The calculator will show a numerical value and also a simplified multiple of $\pi$ ; that simplified multiple is the cone's volume in cubic centimeters.

Step-by-step Explanation

Recall the cone volume formula

For a right circular cone with radius $r$ and height $h$ , the volume formula is

V = \frac{1}{3}\pi r^2 h

This comes from taking one-third of the volume of a cylinder with the same base and height.

Identify and substitute the given values

From the problem:

Radius $r = 6$ centimeters
Height $h = 8$ centimeters

Substitute these into the formula:

V = \frac{1}{3}\pi (6)^2 (8)

Simplify the numeric part step by step

First square the radius:

(6)^2 = 36

Now multiply $36$ by $8$ :

36 \times 8 = 288

So the volume becomes:

V = \frac{1}{3}\pi \cdot 288

Apply the one-third factor and state the final volume

Now divide $288$ by $3$ :

\frac{288}{3} = 96

So the volume is

V = 96\pi

Therefore, the volume of the cone is $96\pi$ cubic centimeters, which corresponds to choice C.

Question 80·Medium·Math

Strategy

Hints

Desmos Guide

Step-by-step Explanation

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Strategy

Hints

Desmos Guide

Step-by-step Explanation