Question

The radius of a metallic sphere is 21 cm . is melted and recast into 27sphere . find the surface area of each small sphere

Answer 1

Volume of sphere$= \frac {4}{3} \pi r^{3}$

Let the radius of Large sphere be R

and radius of small equal 27 spheres be r

Volume of Large sphere = Volume of all 27 Spheres

$\frac {4}{3} \pi R^{3} = 27 × \frac {4}{3} \pi r^{3}$

Here R = 21

Therefore ,

$21^{3} = 27 × r^{3}$

$r^{3} = 7^{3}$

r = 7 cm

Surface area of sphere = $4 \pi r^{2}$

Surface area of 1 small sphere = $4 × \frac {22}{7} × 7^{2} = 616 cm^{2}$

Answer 2

Volume of sphere

Let the radius of Large sphere be R

and radius of small equal 27 spheres be r

Volume of Large sphere = Volume of all 27 Spheres

Here R = 21

Therefore ,

r = 7 cm

Surface area of sphere = 4

Surface area of 1 small sphere =