Question

Hey! can someone give me a step-by-step explanation on how to solve this problem correctly? I know for a fact that I did it incorrectly.

Answer 1

Answer:

B. 1:18

Explanation Down Below

Step-by-step explanation:

Hello!

First, let's find the volume of each cylinder by plugging in the given values.

Volume of a Cylinder: $V = \pi r^2h$

Cylinder A

Since the variables are the same as given in the formula, we can just use the formula as the volume.

$\implies{\boxed{{V = \pi r^2h}}$

Cylinder B

We have to plug in 3r for the radius, and 2h for the height.

• $V = \pi r^2 h$
• $V = \pi (3r)^2(2h)$
• $V = \pi(9r^2)(2h)$
• $V = 18\pi r^2h$

$\implies \boxed{ V = 18\pi r^2h}$

Ratio

We can see that the Volume of Cylinder B is just 18 times the Volume of Cylinder A, but we can find the same ratio using equations.

• $\text{Ratio} = A:B$
• $\text{Ratio} = \pi r^2h: 18\pi r^2h$
• $\text{Ratio} = \frac{\pi r^2h}{18\pi r^2h}$
• $\text{Ratio} = \frac{\not{\pi}\not {r^2}\not{h}}{18\not{\pi}\not{r^2}\not{h}}$
• $\text{Ratio} = \frac1{18}$
• $\text{Ratio} =1:18$

The answer is Option B. 1:18.

Answer 2

Perhaps the 3 from the radius was squared to 9, and then multiplied by the 2 from the height to get 18 in the “1:18”
This is just a guess in case no one else answers your question you can try this