Question

A cylinder and a cone have equal bases. The height of the cylinder is 3 cm and the area of its base is 100 cm2 .The cone is placed upon the cylinder. Volume of the solid figure so formed is 500 cm3 . Find the total height of the figure

Answer 1

Height of the cylinder, h = 3 cm
Let the radius of the cylinder be r cm and the height of the cone be H cm.
Area of the base of cylinder = 100 cm²

$$\therefore \pi r^2=100$$   .....(1) 
The volume of the solid figure = 500 cm³
∴ Volume of the cylinder + Volume of the cone = 500 cm³ 

$$\Rightarrow \pi r^{2}h+\frac{1}{3}\pi r^{2}H=500$$
$$\Rightarrow \pi r^2(h+\frac{H}{3})=500$$
$$\Rightarrow 100(3+\frac{H}{3})=500\left[\text{ Using }\left(1\right)\right]$$
$$\Rightarrow 3+\frac{H}{3}=\frac{500}{100}=5$$
$$\Rightarrow \frac{H}{3}=5-3=2$$
$$\Rightarrow H=6$$ cm

∴ Total height of the figure = h + H = 3 + 6 = 9 cm

Thus, the total height of the figure is 9 cm.