Question

if a cylinder has a volume of 150π cubic cm and the height is 10 cm, what is the radius?
a. 4.79 cm
b. 1.50 cm
c. 5.42 cm
d. 3.87 cm
if a cylinder has a height of 12 cm and a radius of 5 cm, what is the volume in cubic cm?
a. 60π
b. 150π
c. 240π
d. 300π

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.

First - question:

Step1: Substitute given values into formula

Given $V = 150\pi$ and $h = 10$. Substitute into $V=\pi r^{2}h$: $150\pi=\pi r^{2}\times10$.

Step2: Solve for $r^{2}$

Divide both sides of the equation $150\pi = 10\pi r^{2}$ by $10\pi$. We get $\frac{150\pi}{10\pi}=r^{2}$, so $r^{2}=15$.

Step3: Solve for $r$

Take the square - root of both sides. $r=\sqrt{15}\approx 3.87$ cm.

Second - question:

Step1: Substitute given values into formula

Given $r = 5$ and $h = 12$. Substitute into $V=\pi r^{2}h$: $V=\pi\times5^{2}\times12$.

Step2: Calculate the volume

First, $5^{2}=25$. Then $V=\pi\times25\times12 = 300\pi$ cubic cm.

Answer:

First question: d. 3.87 cm
Second question: d. $300\pi$