Question

a cylindrical container has a volume of 400 cubic centimeters and a radius of 5 centimeters. what is the height of the container? use 3.14 for π. round your answer to the nearest tenth.
use the keypad to type your answer in the box provided.
the height of the container is centimeters.

Explanation:

Step1: Write the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

We know that \(V = 400\) \(cm^{3}\), \(r = 5\) \(cm\), and \(\pi=3.14\). Substituting these values into \(V=\pi r^{2}h\), we get \(400=3.14\times5^{2}\times h\).
First, calculate \(5^{2}=25\). Then the equation becomes \(400 = 3.14\times25\times h\).
Next, calculate \(3.14\times25=78.5\). So the equation is \(400=78.5h\).

Step3: Solve for \(h\)

To find \(h\), we use the formula \(h=\frac{V}{\pi r^{2}}\). From \(400 = 78.5h\), we can solve for \(h\) by \(h=\frac{400}{78.5}\).
\(h=\frac{400}{78.5}\approx5.1\)

Answer:

\(5.1\)