Question

A solid right circular cylinder of radius 8 cm and height 2 cm is melted and cast into a right circular cone of height 3 times that of the cylinder. Find the curved surface of the cone ? 

(a) 54 π cm² 

(b) 80 π cm²

(c) 72 π cm²

(d) 77 π cm²

Answer 1

(b) 80π cm²

For cylinder, radius (r₁) = 8 cm, height (h₁) = 2 cm 

For cone, radius (r₂) = ?, height (h₂) = 6 cm 

Now, Volume of cone = Volume of cylinder

⇒ \(\frac13πr^2_2h_2= πr^2_1h_1\) ⇒ \(\frac13πr^2_2\times6 = ​​π\times8\times8\times2\)

⇒ \(r^2_2=\frac{π\times8\times8\times2\times3}{π\times6}=64\) ⇒ r₂ = 8 cm

Curved surface of cone = πr₂l = \(πr_2\sqrt{h^2_2+r^2_2}\)

= π x 8 x \(\sqrt{36\times64}=(π\times8\times10)\)cm² = 80π cm².