Find the volume of a right circular cone that has a height of 5.7 m and a base with a circumference of 2.3 m. Round your answer to the nearest tenth of a cubic meter

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daladaher1234

College

Find the volume of a right circular cone that has a height of 5.7 m and a base with a circumference of 2.3 m. Round your answer to the nearest tenth of a cubic meter.

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mberisso

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Answer:
Volume of the cone is approximately 0.8 cubic meters
Step-by-step explanation:
Recall that the volume of a circular cone is defined by:
$V=\pi R^2\,\frac{H}{3}$
where R is the radius of the cone's base, and H the cone's height. Since we have the information of the height H (5.7 m) we just need to find the radius R. We can do such by using the other piece of information: the circumference of its base.
The circumference of a circle is the product: $2\,\pi\,R$
So by knowing the circumference's length (2.3 m) we can solve for the radius R:
$2.3\,m=2\,\pi\,R\\R=\frac{2.3}{2\,\pi} \,m\\R=0.366\,m$
We can now use this result in the formula for the volume:
$V=\pi ^2\,\frac{H}{3}\\V=\pi (0.366)^2\,\frac{5.7}{3}\,m^3\\V=0.7995868\, m^3$ which can be rounded to the nearest tenth as:
$V=0.8\,m^3$
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