Question

A solid hemisphere of wax with radius 12cm is melted and made into a cone of base radius 6cm compute the height of the cone?

Answer 1

$\frac{1}{2} \times \frac{4}{3} \times 3.14 \times (12 \times 12 \times 12)cm$
1/2*volume of solid sphere

of the semi solid sphere...
V=3619.11cm^3

Now,
h= height
r=6cm

$v = \pi \: { r}^{2} \frac{h}{3}$
Vol of solid cone ...


$3619.11 = 3.14 \times {6}^{2} \times \frac{h}{3}$

$h = \frac{3 \times 3619.11}{3.14 \times 36}$

h=96.04 cm

Answer 2

Answer:

64 cm

Step-by-step explanation:

Radius of hemisphere = 12 cm

Volume of hemisphere = 2/3 π r^3

                                        = (2/ 3) *3.14 * (12)^3

                                        =3617.28 cubic cm.

Radius of cone =  6cm

volume of cone = 1/2  π r^2 *h

                          =(1/2)*3.14* 6^2 *h

                          =56.52 *h cubic cm

Since we are given that hemisphere is melted into cone

So, volume will remain same

So, 3617.28 =56.52 *h

(3617.28)/(56.52) =h

64 = h

Hence the height of the cone is 64 cm.