Question

An ice cream cone is the union of a right circular cone and a hemisphere that has the same circular base as the cone. Find the volume of the ice cream, if the height of the cone is $9cm$ and the radius of its base is $2.5cm$.

Answer 1

Since the conical part and hemispherical part have the same base, their radii will be same, i.e.,

$r=2.5cm$

Also,

Height of the conical part of the ice cream $\left(h\right)=9cm$

Now,

Volume of conical part of ice cream $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times {\left(2.5\right)}^2\times 9$

$=58.93{cm}^3$

Volume of hemispherical part of ice cream $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times {\left(2.5\right)}^3$

$=32.73{cm}^3$

Therefore,

Volume of ice cream $=32.73+58.93=91.66{cm}^3$