Question

By melting 504 cones with diameter 3.5 cm and height 3 cm each, a metallic sphere is recasted. Find the diameter of sphere. Also find the surface area of the sphere. \(\left( take\pi =\frac { 22 }{ 7 } \right) \)

Answer 1

Given,

Diameter of cone = 3.5 cm

∴ Radius (r) = \(\frac { 3.5 }{ 2 }\) cm

Height (h) = 3 cm

∴ Volume of each cone = \(\frac { 1 }{ 3 }\)πr²h

= \(\frac { 1 }{ 3 }\) × \(\frac { 22 }{ 7 }\) × \({ \left( \frac { 3.5 }{ 2 } \right) }^{ 2 }\) × 3 = 9.625 cm³

∴ Volume of 504 cones 

= 504 × 9.625 = 4851 cm³

Now, Let the radius metallic sphere be R

According to the question

Volume of sphere = Volume of 504 cones

Diameter of sphere = 2R = 2 × 10.5 = 21 cm

∴ Surface area of sphere

= 4πR² = 4 × \(\frac { 22 }{ 7 }\) × (10.5)²

= 1386 cm²