Question

12 solid spheres of the same radii are made by melting a solid metallic cylinder of base diameter 2cn and height 16cm. Find the diameter of the each sphere. ​

Answer 1

Given :-

• Base diameter of solid metallic cylinder - 2cm .
• Height of cylinder - 16cm .

To Find :-

• Diameter of each sphere.

Solution :-

Base diameter of cylinder = 2cm

Radius (R1) = $\dfrac{D}{2}$ = $\dfrac{2}{2}$ = 1cm

Height of cylinder = 16cm

Volume of cylinder = πr²h

Now,

Volume of spheres = ${\bold{\frac{4}{3}πr²}}$

Volume of 12 spheres = 12 × ${\bold{\frac{4}{3}πr²}}$

Let radius of spheres be = R2

A.T.Q.

Volume of 12 spheres = volume of cylinder

=> 12 × ${\bold{\frac{4}{3}πr2²}}$ = πr1²h

=> 4 × 4πr2² = πr1²h

=> 16πr2² = πr1²h

=> 16r2² = r1²h (cancelling π from both sides)

=> 16r2² = (1)² × 16

=> 16r2² = 16

=> r2² = 1 (cancelling 16 from both sides)

=> r = √1

=> r = 1cm

Diameter of each sphere = 2r = 2 × 1 = 2cm

Hence, Diameter of each sphere is 2cm .