Question

find the volume of a right circular cone that has a height of 11.8 ft and a base with a radius of 16 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a right circular cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Identify the given values

We are given that the radius \( r = 16\) ft and the height \( h=11.8\) ft.

Step3: Substitute the values into the formula

Substitute \( r = 16\) and \( h = 11.8\) into the formula:

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First, calculate \( 256\times11.8 = 256\times(10 + 1.8)=2560+460.8 = 3020.8\)
Then, \( V=\frac{1}{3}\times\pi\times3020.8\)

$$ V=\frac{3020.8\pi}{3}\approx\frac{3020.8\times3.14159}{3} $$

Calculate \( 3020.8\times3.14159\approx3020.8\times3 + 3020.8\times0.14159=9062.4+427.79\approx9490.19\)
Then, \( V\approx\frac{9490.19}{3}\approx3163.4\) (rounded to the nearest tenth)

Answer:

\( 3163.4\)