Question

A metallic sphere of radius 4.2 cm. is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Answer 1

Given, sphere converted into cylinder. 

Hence volume of the sphere = volume of the cylinder. 

Sphere: 

Radius, r = 4.2 cm

Volume V = \(\frac{4}{3}\)πr³ 

= \(\frac{4}{3}\) × \(\frac{22}{7}\) × 4.2 × 4.2 × 4.2 

= 4 × 22 × 0.2 × 4.2 × 4.2 

= 4 x 22 x 0.2 x 4.2 x 4.2 

= 310.464 

Cylinder: 

Radius, r = 6 cm 

Height h = h say 

Volume = πr²h 

= \(\frac{22}{7}\) × 6 × 6 × h 

= \(\frac{22\times36}{7}h\)

= \(\frac{792}{7}h\)

Hence, \(\frac{792}{7}h\)= 310.464 

h = \(\frac{310.464\times7}{792}h\)= 2.744cm 

!! π can be cancelled on both sides i.e., sphere = cylinder