### Home > CC3 > Chapter Ch10 > Lesson 10.1.3 > Problem10-41

10-41.

Find the volume of the cone shown in problem .

From problem , you learned that the volume of a cone is one-third the volume of a cylinder with the same base area and height.

The equation for the volume of a cylinder is:
$\text{Volume = (area of base)(height)}$
So the volume of a cone is:

$\text{Volume } =\; \frac{1}{3}(\text{area of base})(\text{height})$

The base is a circle with a radius of 6 inches. So using the equation for area of a circle:
$\text{Area of base} = (6^2)π= 36π$

The height of the cylinder is $8$ inches. Substitute the known values into the volume equation for a cone:

$\text{Volume}=\frac{1}{3}(36\pi )(8)$

Now simplify to get the answer.
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