Question

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom . Find the volume of water left in the cylinder , if the radius of the cylinder is equal to the radius of te cone .

Answer 1

Height of the cone, h = 120 cm
Radius of the cone, r = 60 cm
Height of the cylinder, H = 180 cm
Radius of the cylinder, R = 60 cm
Volume of the cylinder = ${\mathrm{\pi R}}^2\mathrm{H}=\mathrm{\pi }{\left(60\right)}^2\times 180{\mathrm{cm}}^3$
Volume of the cone = $\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\mathrm{\pi }{\left(60\right)}^2\times 120$
Volume of water left in the cylinder = Volume of cylinder − volume of the cone
$$\begin{gathered} =\mathrm{\pi }{\left(60\right)}^2\times 180-\frac{1}{3}\mathrm{\pi }{\left(60\right)}^2\times 120 \\ =\mathrm{\pi }{\left(60\right)}^2\left[180-40\right] \\ =\mathrm{\pi }\times 3600\left[140\right] \\ =1584000{\mathrm{cm}}^3 \\ =1.584{\mathrm{m}}^3 \end{gathered}$$