Question

1. a cylinder has a height of 5 cm and a volume of 135π cm³. what is the radius of the cylinder?

a. 5.2 cm
b. 3.5 cm
c. 2.9 cm
d. 4.6 cm

Explanation:

Step1: Recall volume formula for cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We are given $V = 135\pi$ $cm^{3}$ and $h=5$ cm. Substituting into the formula gives $135\pi=\pi r^{2}\times5$.

Step3: Solve for $r^{2}$

Divide both sides of the equation by $5\pi$. $\frac{135\pi}{5\pi}=r^{2}$, so $r^{2}=27$.

Step4: Solve for $r$

Take the square - root of both sides. $r=\sqrt{27}\approx5.2$ cm.

Answer:

a. 5.2 cm