Question

a cylinder has a height of 5 cm and a volume of 135π cm³. what is the radius of the cylinder?
a. 3.5 cm
b. 5.2 cm
c. 2.9 cm
d. 4.6 cm

a cylindrical container has a volume of 500π cm³. if the height is 20 cm, what is the diameter?
a. 15
b. 20
c. 5
d. 10

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Solve first problem for radius

Given $V = 135\pi$ and $h = 5$. Substitute into formula: $135\pi=\pi r^{2}\times5$. Divide both sides by $5\pi$: $\frac{135\pi}{5\pi}=r^{2}$, so $r^{2}=27$, and $r=\sqrt{27}\approx 5.2$ cm.

Step3: Solve second problem for radius then diameter

Given $V = 500\pi$ and $h = 20$. Substitute into formula: $500\pi=\pi r^{2}\times20$. Divide both sides by $20\pi$: $\frac{500\pi}{20\pi}=r^{2}$, so $r^{2}=25$, then $r = 5$ cm. Since $d = 2r$, $d=10$ cm.

Answer:

1. b. 5.2 cm
2. d. 10