Question

The radius of a right circular cylinder increased by $50\% $ . Find the % increase in volume
$A.120\% $
$B.125\% $
$C.150\% $
$D.130\% $

Answer 1

Hint: Volume of the cylinder is directly proportional to the square of the radius of the cylinder and directly proportional the height of the cylinder.

Complete step-by-step answer:
Volume of cylinder = $\pi {{\text{r}}^2}h$
Percentage change =$\dfrac{{New{\text{ value - Original value}}}}{{Original{\text{ value}}}}{\text{ }} \times {\text{ 100}}$
Step By Step Solution:
Let the radius of the cylinder is 2r and the height of the cylinder is h.
Original Volume of the cylinder = $\pi {({\text{2r)}}^2}{\text{h}}$= $4\pi {r^2}h$
As radius is increased by $50\% $,
So, the change in radius = $\dfrac{{2r \times 50}}{{100}}$=$r$
Increased radius = ${\text{2r + r}}$=$3r$
Now, the new volume of the cylinder =$\pi {{\text{(3r)}}^2}h$ =$9\pi {r^2}h$
Percentage change in volume ;
$=\dfrac{{New{\text{ value - Original value}}}}{{Original{\text{ value}}}}{\text{ }} \times {\text{ 100}}$
$=\dfrac{{9\pi {r^2}h - 4\pi {r^2}h}}{{4\pi {r^2}h}} \times 100$
$=\dfrac{{5\pi {r^2}h}}{{4\pi {r^2}h}} \times 100$
$=125$
So, the percentage increase in the volume is $125\% $ .

Note: A cylinder has two same circular surfaces at the top and bottom and a curved surface between them. Another way is we can assume the radius of the cylinder=100cm solved by the given condition. Both ways we will get the same answer.