Question

1. a cone has a diameter of 22 inches and a height of 15 inches. enter the volume for the cone. round your answer to the nearest hundredths if necessary.

Explanation:

Step1: Find the radius of the cone

The diameter \( d = 22 \) inches, so the radius \( r=\frac{d}{2}=\frac{22}{2} = 11 \) inches.

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. Here, \( r = 11 \) inches and \( h=15 \) inches.

Step3: Substitute the values into the formula

Substitute \( r = 11 \) and \( h = 15 \) into the formula:

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Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V\approx605\times3.14159\approx1900.66 \) (rounded to the nearest hundredth)

Answer:

\( 1900.66 \) cubic inches (or if we use \( \pi = 3.14 \), \( V=\frac{1}{3}\times3.14\times121\times15=\frac{1}{3}\times3.14\times1815 = 3.14\times605=1900.7 \), but the more accurate value with \( \pi\approx3.14159 \) is approximately \( 1900.66 \))