Question

the volume of a cone is one - third the volume of a cylinder and is calculated using the formula

v = \frac{1}{3}pi r^{2}h

where ( v ) represents the volume of the cone, ( r ) is the radius of the base, and ( h ) is the height of the cone.

a cone - shaped pile of sand has a volume of 315 cubic feet. if its height is 14 feet, find the radius of the piles base. use 3.14 for ( pi ). round your answer to the nearest tenth.

use the keypad to type your answer in the box provided.

the radius of piles base is (square) feet.

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 315\), \(h=14\), \(\pi = 3.14\), and the formula \(V=\frac{1}{3}\pi r^{2}h\).
Substitute: \(315=\frac{1}{3}\times3.14\times r^{2}\times14\)

Step2: Simplify the right - hand side

First, calculate \(\frac{1}{3}\times3.14\times14\):
\(\frac{1}{3}\times3.14\times14=\frac{3.14\times14}{3}=\frac{43.96}{3}\approx14.65\)
The equation becomes \(315 = 14.65r^{2}\)

Step3: Solve for \(r^{2}\)

\(r^{2}=\frac{315}{14.65}\approx21.5\)

Step4: Solve for \(r\)

\(r=\sqrt{21.5}\approx4.6\)

Answer:

\(4.6\)