Question

The radius as well as the height of a circular cone increases by 10%. The percentage increases in its volume is

• A.
  $17.1$
• B.
  $21.0$
• C.
  $33.1$
• D.
  $72.8$

Answer 1

The correct option is C

$33.1$
We know formula for volume of a (right circular) cone is

$\frac{1}{3}\pi r^{2}h$

Original volume,

$V_0=\frac{1}{3}\pi r_1^2{h}_1$

Now we know radius and height both are increased by $10$%. So after increase the new volume is

$V_n=\frac{1}{3}\pi \left(1.1r_1{)}^2\right(1.1)h_1$

$=1.331\left(\frac{1}{3}\pi r_1^2{h}_1\right)$

$=1.331\left(V_0\right)$

% change in volume

$=\frac{V_n-V_0}{V_0}\times 100$

$=\frac{1.331V_0-V_0}{V_0}\times 100=33.1$