Question

The radius and height of a right circular cylinder are each increased by 20%. What percentage increase is in the volume?

Answer 1

hope it will help u.... m

Answer 2

Answer:

The percentage increase in the volume is 72.8%.

Step-by-step explanation:

Given : The radius and height of a right circular cylinder are each increased by 20%.

To find : What percentage increase is in the volume?

Solution :

Let the radius be 'r' and height of the cylinder be 'h'.

Volume of the cylinder is $V=\pi r^2h$

The radius and height of a right circular cylinder are each increased by 20%.

New radius is $r_n=r+\frac{20}{100}r=\frac{6}{5}r$

New height is $h_n=h+\frac{20}{100}h=\frac{6}{5}h$

New volume is given by,

$V_n=\pi(\frac{6}{5}r)^2(\frac{6}{5}h)$

$V_n=\frac{216}{125}\pi r^2 h$

Increase in volume is given by

$V_I=V_n-V$

$V_I=\frac{216}{125}\pi r^2 h-\pi r^2 h$

$V_I=\frac{91}{125}\pi r^2 h$

Percentage increase is

$P\%=\frac{V_I}{V}\times 100$

$P\%=\frac{\frac{91}{125}\pi r^2 h}{\pi r^2 h}\times 100$

$P\%=\frac{91}{125}\times 100$

$P\%=72.8\%$

Therefore, the percentage increase in the volume is 72.8%.