Question

The radius of a cylinder is increased by a factor of 3. The height of the cylinder is increased by a factor of 2. What is the effect of the increases on the volume of the cylinder? A) The volume of the cylinder increases by a factor of 6. B) The volume of the cylinder increases by a factor of 18. C) The volume of the cylinder increases by a factor of 12. D) The volume of the cylinder increases by a factor of 3 2 .

Answer 1

Answer:

The answer is the option B

The volume of the cylinder increases by a factor of $18$

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

$V1=\pi r^{2}h$ ------> original volume

In this problem

$h=2h\ units$

$r=3r\ units$

substitute in the formula

$V2=\pi (3r)^{2}(2h)$

$V2=18\pi r^{2}h$  

$V2=18V1$  

therefore

The volume of the cylinder increases by a factor of $18$

Answer 2

The volume of the cylinder increases by a factor of 18. Option (B) is correct.

Further explanation:

Given:

The radius of the cylinder is ${\text{4 units}}$ and the height of the cylinder is ${\text{6 units}}.$

The options are given as follows.

A. The volume of the cylinder increases by a factor of 6.

B. The volume of the cylinder increases by a factor of 18.

C. The volume of the cylinder increases by a factor of 12.

D. The volume of the cylinder increases by a factor of 32.

Explanation:

The formula for the volume of the cylinder can be expressed as,

$\boxed{{\text{Volume}} = \pi {r^2}h}$

Here, ‘$r$” represents the radius of the cylinder and “$h$” represents the height of the cylinder.

The radius increased by a factor of 3.

The height increased by a factor of 2.

The new volume of the cylinder can be obtained as follows,

$\begin{aligned}{\text{Final Volume}} &= \pi {\left( {3r} \right)^2}\left( {2h} \right)\\&=\pi\times \left( {9{r^2}} \right) \times \left( {2h} \right)\\&= 18\pi {r^2}h\\&= 18 \times {\text{Volume}}\\\end{aligned}$

The volume of the cylinder increases by a factor of 18. Option (B) is correct.

Option A is not correct.

Option B is correct.

Option C is not correct.

Option D is not correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Mensuration

Keywords: Cylinder, surface area of the cylinder, volume of the cylinder, right cylinder, height, and radius depth, radius of cylinder, increased factor of 3, increased factor of 2, increase effect on volume.