Question

by melting two spheres of radii 1 cm and 6cm a hollow sphere with thickness 1 cm is made find the external radius of the new sphere​

Answer 1

Volume of two solid metallic spheres = 4π(r1³+r2³)/3

= 4π(1³ + 6³)/3

= 4π(1 + 216)/3

= 4π× 217/3

Internal radius of hollow sphere = r cm (let)

= 4π((r + 1)³ + r³)/3

= 4π× 217/3

⇒ r³+ 3r² + 3r + 1 – r³ = 217

⇒ 3r² + 3r + 1 = 217

⇒ 3r² + 3r – 216 = 0

⇒ r² + r – 72 = 0

⇒ r² + 9r – 8r – 72 = 0

⇒ r (r + 9) – 8 (r + 9) = 0

⇒ (r – 8) (r + 9) = 0

⇒ r = 8 cm. because r ≠ –9

∴ External radius of hollow sphere=9 cm