Question

Find the volume of a right circular cone that has a height of 8.1 in and a base with a diameter of 7.6 in. Round your answer to the nearest tenth of cubic inch

Answer 1

Answer:

$V=122.5in^3$

Step-by-step explanation:

The volume of a right circular cone is given by:

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

where r is the radius of the circle and h is the height of the cone, and $\pi$ is a constant $\pi=3.1416$.

According to the problem the height is:

$h=8.1 in$

and we don't have the radius but we have the diameter, which is useful to find it. We just divide the diameter by 2 to find the radius:

$r=\frac{d}{2}=\frac{7.6in}{3}=3.8in$

Now, we can find the volume by substituting all the known values:

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

$V=\frac{(3.1416)(3.8in)^2(8.1in)}{3} \\\\V=\frac{(3.1416)(14.44in^2)(8.1in)}{3} \\\\V=\frac{367.454in^3}{3} \\\\V=122.485$

Rounding the volume to the nearest tenth of cubic inch we get:

$V=122.5in^3$