Question

the volume of this cone is 251.2 cubic centimeters. what is the height of this cone? round your answer to the nearest hundredth. 4 cm h≈ centimeters

Explanation:

Step1: Recall the volume formula of a cone

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

Step2: Substitute the known values into the formula

Given \( V = 251.2\space cm^{3}\), \( r=4\space cm\), and \(\pi\approx3.14\).
Substitute into \( V=\frac{1}{3}\pi r^{2}h\), we get \( 251.2=\frac{1}{3}\times3.14\times4^{2}\times h\).
First, calculate \(4^{2}=16\), then \(\frac{1}{3}\times3.14\times16=\frac{3.14\times16}{3}=\frac{50.24}{3}\).
The equation becomes \(251.2=\frac{50.24}{3}h\).

Step3: Solve for \( h \)

Multiply both sides of the equation by \(3\): \(251.2\times3 = 50.24h\).
\(753.6 = 50.24h\).
Then divide both sides by \(50.24\): \(h=\frac{753.6}{50.24}\).
\(h = 15.00\)

Answer:

\(15.00\)