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 hat has a volume of 100 cubic inches, and its base radius is 3 inches what is the height of the hat? use 3.14 for ( pi ). round your answer to the nearest tenth.

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

the height of the hat is ( square ) inches.

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 100\), \(r = 3\), and \(\pi=3.14\) into \(V=\frac{1}{3}\pi r^{2}h\). So, \(100=\frac{1}{3}\times3.14\times3^{2}\times h\).

Step2: Simplify the equation

First, calculate \(3^{2}=9\). Then \(\frac{1}{3}\times3.14\times9 = 3.14\times3=9.42\). The equation becomes \(100 = 9.42h\).

Step3: Solve for \(h\)

Divide both sides of the equation \(100 = 9.42h\) by \(9.42\). So, \(h=\frac{100}{9.42}\approx10.6\).

Answer:

\(10.6\)