Respuesta :
Answer:
The answer is the option B
The volume of the cylinder increases by a factor of [tex]18[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V1=\pi r^{2}h[/tex] ------> original volume
In this problem
[tex]h=2h\ units[/tex]
[tex]r=3r\ units[/tex]
substitute in the formula
[tex]V2=\pi (3r)^{2}(2h)[/tex]
[tex]V2=18\pi r^{2}h[/tex]
[tex]V2=18V1[/tex]
therefore
The volume of the cylinder increases by a factor of [tex]18[/tex]
The volume of the cylinder increases by a factor of 18. Option (B) is correct.
Further explanation:
Given:
The radius of the cylinder is [tex]{\text{4 units}}[/tex] and the height of the cylinder is [tex]{\text{6 units}}.[/tex]
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,
[tex]\boxed{{\text{Volume}} = \pi {r^2}h}[/tex]
Here, ‘[tex]r[/tex]” represents the radius of the cylinder and “[tex]h[/tex]” 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,
[tex]\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}[/tex]
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:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function https://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.
