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Chapter 1: Problem 24

Find the volume of a cone with a radius of 6 in. and a height of 13 in

Short Answer

Expert verified
The volume of the cone is approximately 490.088 cubic inches.

Step by step solution

01

- Identify the formula for the volume of a cone

The volume of a cone is calculated using the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cone.
02

- Substitute the given values into the formula

Substitute the given radius \( r = 6 \) inches and height \( h = 13 \) inches into the formula: \[ V = \frac{1}{3} \pi (6)^2 (13) \]
03

- Simplify the expression

Calculate the area of the base: \[ (6)^2 = 36 \] Multiply by the height: \[ 36 \times 13 = 468 \] Then multiply by \( \frac{1}{3} \): \[ \frac{1}{3} \times 468 = 156 \] Hence, the volume is: \[ V = 156 \pi \]
04

- Provide the numerical answer

Using the value of \( \pi \approx 3.1416 \), calculate the volume: \[ V \approx 156 \times 3.1416 \approx 490.088 \] Therefore, the volume of the cone is approximately 490.088 cubic inches.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

cone volume formula
Understanding how to find the volume of a cone starts with knowing the formula. The formula to calculate the volume is:
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Most popular questions from this chapter

The regular price of a 14 -piece cookware set is \(\$ 728\). It is on sale at a discount of \(35 \%\). The sales tax is \(6.5 \%\). Find the final cost of the cookware including tax. Round to the nearest hundredth.

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Find the circumference of a circle with a radius of \(0.5 \mathrm{in}\).

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