Question

what is the approximate volume of a cone with a radius of 7 inches and a height of 10 inches?
a 513.1 cubic inches
b 733.0 cubic inches
c 1,593.3 cubic inches
d 2,199.1 cubic inches

Explanation:

Step1: Recall the volume formula for a cone

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

Step2: Substitute the given values into the formula

Given \( r = 7 \) inches and \( h=10 \) inches. Substitute into the formula: \( V=\frac{1}{3}\times\pi\times(7)^{2}\times10 \).
First, calculate \( (7)^{2}=49 \). Then the formula becomes \( V=\frac{1}{3}\times\pi\times49\times 10=\frac{490}{3}\pi \).

Step3: Approximate the value

Take \( \pi\approx3.14 \). Then \( V=\frac{490}{3}\times3.14 \).
\( \frac{490\times3.14}{3}=\frac{1538.6}{3}\approx512.87\approx513.1 \) (using more precise \( \pi\) value in calculation can lead to slight difference, if we use \( \pi = 3.1416\), \( \frac{490\times3.1416}{3}=\frac{1539.384}{3}=513.128\approx513.1 \))

Answer:

A. 513.1 cubic inches