Question

1. a cylinders volume is 250π cm³ and its radius is 5 cm. what is its height?

a. 20 cm
b. 12 cm
c. 10 cm
d. 25 cm

Explanation:

Step1: Recall the volume formula 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 \(V = 250\pi\space cm^{3}\) and \(r = 5\space cm\). Substitute into \(V=\pi r^{2}h\), we get \(250\pi=\pi\times(5)^{2}\times h\).

Step3: Simplify the equation

First, \(\pi\times(5)^{2}\times h=\pi\times25\times h\). The equation becomes \(250\pi = 25\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation \(250\pi = 25\pi h\) by \(25\pi\). \(\frac{250\pi}{25\pi}=h\), so \(h = 10\space cm\).

Answer:

C. 10 cm