if the radius and height of a cylinder are increased by 10 % and decreased by 5% then what percentage change in volume(with steps pls)
Answers
Step-by-step explanation:
The percentage change in the volume is 6.4%.
Step-by-step explanation:
Given : If the radius of a cylinder is increased by 20% and its height is decreased by 10%.
To find : What is the percentage change in the volume?
Solution :
Let r be the radius of cylinder is increased by 20%
i.e, \frac{120}{100}=\frac{6}{5}
100
120
=
5
6
The old radius is 5 and new radius is 6.
Let h be the height of cylinder is increased by 10%
i.e, \frac{110}{100}=\frac{11}{10}
100
110
=
10
11
The old height is 10 and new height is 11.
The volume of old cylinder with r=5 and h=10
V_o=\pi r^2 hV
o
=πr
2
h
V_o=\pi\times 5^2\times 10V
o
=π×5
2
×10
V_o=\pi\times 25\times 10V
o
=π×25×10
V_o=250\piV
o
=250π
The volume of new cylinder with r=6 and h=11
V_n=\pi r^2 hV
n
=πr
2
h
V_n=\pi\times 6^2\times 11V
n
=π×6
2
×11
V_n=\pi\times 36\times 11V
n
=π×36×11
V_n=234\piV
n
=234π
Volume change is
V_o-V_n=250\pi -234\pi=16\piV
o
−V
n
=250π−234π=16π
Percentage change is
\frac{16\pi}{250\pi} \times 100=6.4\%
250π
16π
×100=6.4%
Therefore, The percentage change in the volume is 6.4%.