Question

find the volume of a right circular cone that has a height of 7.4 in and a base with a diameter of 5.4 in. round your answer to the nearest tenth of a cubic inch.

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

We know that the diameter \( d = 5.4 \) in. The radius \( r \) is half of the diameter, so \( r=\frac{d}{2}=\frac{5.4}{2} = 2.7 \) in.

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

We are given that \( h = 7.4 \) in, \( r=2.7 \) in. Substituting these values into the formula \( V=\frac{1}{3}\pi r^{2}h \), we get:

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Step4: Calculate the numerical value and round to the nearest tenth

Using \( \pi\approx3.14159 \), we have \( V\approx17.982\times3.14159\approx56.5 \) (rounded to the nearest tenth).

Answer:

\( 56.5 \) cubic inches