Question

a cylinder has a height of 9 cm and a volume of 81π cm³. what is the radius of the cylinder?
a. 2cm
b. 4cm
c. 3cm
d. 6cm

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

Given \(V = 81\pi\space cm^{3}\) and \(h=9\space cm\). Substitute into \(V=\pi r^{2}h\), we get \(81\pi=\pi r^{2}\times9\).

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

Divide both sides of the equation \(81\pi=\pi r^{2}\times9\) by \(9\pi\). \(\frac{81\pi}{9\pi}=r^{2}\), so \(r^{2} = 9\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r=\sqrt{9}=3\space cm\).

Answer:

C. 3cm