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 

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

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

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