Question

1. a cylindrical soup can has a volume of 400π cm³ and a radius of 4 cm. what is its height?

a. 25 cm
b. 12 cm
c. 15 cm
d. 20 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, and \(h\) is the height.

Step2: Substitute the given values into the formula

We are given that \(V = 400\pi\space cm^{3}\) and \(r = 4\space cm\). Substituting these into the formula \(V=\pi r^{2}h\), we get \(400\pi=\pi\times(4)^{2}\times h\).

Step3: Simplify the equation

First, simplify \(\pi\times(4)^{2}\times h\) to \(16\pi h\). So the equation becomes \(400\pi=16\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation \(400\pi = 16\pi h\) by \(16\pi\). \(\frac{400\pi}{16\pi}=h\). Since \(\frac{400}{16}=25\), we find that \(h = 25\space cm\).

Answer:

A. 25 cm