Question

a cylinder has a radius of 2 yards. its volume is 12.56 cubic yards. what is the height of the cylinder?
round your answer to the nearest hundredth.
$h=square$ yards

Explanation:

Step1: Write the formula for the volume of a cylinder

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

Step2: Rearrange the formula to solve for \( h \)

We get \( h=\frac{V}{\pi r^{2}} \).

Step3: Substitute the given values

Given \( V = 12.56 \) cubic yards and \( r = 2 \) yards. Substitute into the formula: \( h=\frac{12.56}{\pi\times(2)^{2}} \).

Step4: Calculate the value

First, \( (2)^{2}=4 \), then \( \pi\times4\approx3.14\times4 = 12.56 \). So \( h=\frac{12.56}{12.56}=1.00 \).

Answer:

\( 1.00 \)