Question

solid hemisphere of wax of radius 12 cm is melted and made into a cylinder of its base radius 6 CM calculate the height of the cylinder​

Answer 1

Here in the solid hemisphere of wax is melted and made into cylinder . So ,

Volume of hemisphere = Volume of cylinder

FORMULA:-

Volume of hemisphere

$= \frac{2}{3} \pi {r}^{3}$

Volume of cylinder

$= \pi {r}^{2} h$

GIVEN :-

Hemisphere :

r = 12 cm

Cylinder :

r = 6 cm

TO FIND : -

Height of cylinder (h) = ?

SOLUTION :-

Volume of hemisphere = Volume of cylinder

$= \frac{2}{3} \pi {r}^{3} = \pi {r}^{2} h$

$= \frac{2}{3} \times 12 \times 12 \times 12 \times \pi = \pi \times 6 \times 6 \times \times h$

$= \frac{2}{3} \times 12 \times 12 \times 12 = 6 \times 6 \times h$

$= 2 \times 4 \times 12 \times 12 = 6 \times 6 \times h$

$= h = \frac{2 \times 4 \times 12 \times 12}{6 \times 6}$

$= h = 2 \times 4 \times 2 \times 2$

$= h = 32 \: cm$