Question

27 solid iron spheres, each of radius 'xcm' are melted to form a sphere with radius 'ycm'. find the ratio x:y.​

Answer 1

Answer:

Radius of 1 solid iron sphere =r

⇒Volume =34πr3

⇒Volume of 27 solid iron spheres =27×34πr3

⇒34πr′3=27×34πr3

r′3=2πr3

⇒r′=3r

(ii) Surface area =4πr2

SA r′=4πr′2

=4π(3r)2=36πr2

S′S=36πr24πr2=91=1:9

Answer 2

Volum of shhere $=\frac{4}{3}\pi r^3$

Given: 1st radius $=xcm$ and second radius $=ycm$

$27\times \frac{4}{3}\pi x^3=\frac{4}{3}\pi y^3$

$\frac{x^3}{y^3} =\frac{1}{27}$

Taking Root

$(\frac{x}{y})^3^\times^\frac{1}{3}=(\frac{1}{27})^\frac{1}{3}$

$\frac{x}{y} =\frac{1}{3}$