Question

1. a cylindrical container has a volume of ( 500pi mathrm{cm}^3 ). if the height is ( 20 mathrm{cm} ), what is the diameter?

( \bigcirc ) a. 15
( \bigcirc ) b. 10
( \bigcirc ) c. 20
( \bigcirc ) d. 5

Explanation:

Step1: Recall the volume formula for 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: Substitute the given values into the formula

We know that \(V = 500\pi\space cm^{3}\) and \(h=20\space cm\). Substituting these into \(V=\pi r^{2}h\) gives \(500\pi=\pi r^{2}\times20\).

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

Divide both sides of the equation \(500\pi=\pi r^{2}\times20\) by \(20\pi\). So, \(r^{2}=\frac{500\pi}{20\pi}=25\).

Step4: Solve for \(r\)

Take the square - root of both sides. Since \(r^{2} = 25\), then \(r=\sqrt{25}=5\space cm\).

Step5: Calculate the diameter

The diameter \(d = 2r\). Substituting \(r = 5\space cm\), we get \(d=2\times5 = 10\space cm\).

Answer:

b. 10