Question

find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 5.2 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: Find the radius of the base

The diameter \( d \) of the base is given as \( 5.2 \) ft. The radius \( r \) is half of the diameter, so \( r = \frac{d}{2}=\frac{5.2}{2}=2.6 \) ft.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know that \( h = 2.5 \) ft, \( r = 2.6 \) ft. Substituting these values into the volume formula:

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Step4: Calculate the volume

First, calculate \( 3.14159\times16.9\approx53.093 \). Then, divide by 3: \( \frac{53.093}{3}\approx17.7 \) (rounded to the nearest tenth).

Answer:

The volume of the right circular cone is approximately \( 17.7 \) cubic feet.