Question

if a cylinders height is doubled and the radius is unchanged, its volume will _____.
a. remain the same
b. halve
c. triple
d. double
what is the height of a cylinder with a volume of 500π cm³ and a radius of 5 cm?
a. 15 cm
b. 12 cm
c. 20 cm
d. 10 cm

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Analyze first - question

Let the original height be $h_1$ and the new height be $h_2 = 2h_1$, with radius $r$ unchanged. Original volume $V_1=\pi r^{2}h_1$, new volume $V_2=\pi r^{2}h_2=\pi r^{2}(2h_1) = 2(\pi r^{2}h_1)=2V_1$. So the volume doubles.

Step3: Analyze second - question

Given $V = 500\pi$ $cm^{3}$ and $r = 5$ $cm$. Substitute into $V=\pi r^{2}h$. We get $500\pi=\pi\times(5)^{2}\times h$. Simplify the right - hand side: $\pi\times(5)^{2}\times h = 25\pi h$. Then solve for $h$ from the equation $500\pi=25\pi h$. Divide both sides by $25\pi$: $h=\frac{500\pi}{25\pi}=20$ $cm$.

Answer:

1. d. double
2. c. 20 cm