Question

A solid hemisphere of wax of radius 12 cm is melted and made into a cylinder of its base radius 6 cm. Calculate the height (in cm) of the cylinder.

Answer 1

Hint: Here we will use the condition i.e., volume of the sphere is equal to volume of cylinder as the solid hemisphere of wax is melted and made into a cylinder.

Complete step-by-step answer:
So, Volume of hemisphere= Volume of Cylinder.
Formula:
Volume of sphere= $\dfrac{2}{3}\pi {r_1}^3$ (${r_1}$= radius of hemisphere)
Volume of cylinder= $\pi {r_2}^2h$ (${r_2}$= radius of cylinder, h= height of cylinder)
Given:
Hemisphere: ${r_1} = 12cm$
Cylinder: ${r_2} = 6cm$
h=?
We have to find height as asked. So
$\dfrac{2}{3}\pi {r_1}^3$=$\pi {r_2}^2h$
$
  \dfrac{2}{3} \times \pi \times 12 \times 12 \times 12 = \pi \times 6 \times 6 \times h \\
  2 \times \pi \times 4 \times 12 \times 12 = \pi \times 6 \times 6 \times h \\
  h = \dfrac{{2 \times 4 \times 12 \times 12}}{{6 \times 6}} \\
  h = 2 \times 4 \times 2 \times 2 \\
  h = 32cm \\
$

Note: In these types of problems only the shape of the object changes; the quantity remains unchanged which is the volume. For e.g. take 1 litre water either in a bottle or bucket the volume remains unchanged. So directly compare volumes of both objects and you will get the unknown.