Question

1. the volume of a cylinder is 200π cm³ and its height is 8 cm. what is the radius of the base?

a. 4 cm
b. 10 cm
c. 3 cm
d. 5 cm

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

Step2: Substitute the given values into the formula

Given \(V = 200\pi\space cm^{3}\) and \(h=8\space cm\). Substitute into \(V=\pi r^{2}h\), we get \(200\pi=\pi r^{2}\times8\).

Step3: Simplify the equation

Divide both sides of the equation \(200\pi=\pi r^{2}\times8\) by \(\pi\). The equation becomes \(200 = 8r^{2}\).

Step4: Solve for \(r^{2}\)

Divide both sides of \(200 = 8r^{2}\) by 8. We have \(r^{2}=\frac{200}{8}=25\).

Step5: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r = \sqrt{25}=5\space cm\).

Answer:

D. 5 cm