Question

1. a cone has a height of 9 cm and a radius of 6 cm. what is its approximate volume using \\( \pi = 3.14 \\)?

a. \\( 282.6 \mathrm { cm } ^ { 3 } \\)
b. \\( 169.56 \mathrm { cm } ^ { 3 } \\)
c. \\( 452.16 \mathrm { cm } ^ { 3 } \\)
d. \\( 339.12 \mathrm { cm } ^ { 3 } \\)

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 \(r = 6\) cm, \(h=9\) cm, and \(\pi = 3.14\). Substitute these values into the formula:
\(V=\frac{1}{3}\times3.14\times6^{2}\times9\)
First, calculate \(6^{2}=36\). Then the formula becomes \(V=\frac{1}{3}\times3.14\times36\times9\)

Step3: Simplify the expression

\(\frac{1}{3}\times36 = 12\). So \(V=3.14\times12\times9\)
\(12\times9 = 108\). Then \(V=3.14\times108\)
\(3.14\times108=(3 + 0.14)\times108=3\times108+0.14\times108=324+15.12 = 339.12\) \(cm^{3}\)

Answer:

d. \(339.12\ cm^{3}\)