Question

1. a cylinder has a volume of 1,500 cm³. if its height is 10 cm, what is the radius of its base?

a. 7 cm
b. 4 cm
c. 5 cm
d. 6.9 cm

Explanation:

Step1: Recall 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 of the base, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know \(V = 1500\space cm^{3}\) and \(h=10\space cm\). Substituting these into \(V=\pi r^{2}h\) 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 \(r^{2}\). \(r=\sqrt{47.77}\approx6.9\space cm\).

Answer:

d. \(6.9\space cm\)