Question

a cylinder has a volume of ( 1,500 mathrm{cm}^{3} ). if its height is ( 10 mathrm{cm} ), what is the radius of its base?
a. ( 4 mathrm{cm} )
b. ( 6.9 mathrm{cm} )
c. ( 7 mathrm{cm} )
d. ( 5 mathrm{cm} )

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 of the base, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know that \(V = 1500\space cm^{3}\) and \(h=10\space cm\). Substituting these into the formula gives \(1500=\pi r^{2}\times10\).

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

First, divide both sides of the equation \(1500 = 10\pi r^{2}\) by \(10\pi\). So, \(r^{2}=\frac{1500}{10\pi}=\frac{150}{\pi}\). Taking \(\pi\approx3.14\), we have \(r^{2}=\frac{150}{3.14}\approx47.77\).

Step4: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{47.77}\approx6.9\space cm\).

Answer:

B. \(6.9\space cm\)