A metallic cone is turned into the cylindrical shape with same radius.

1.	A metallic cone is turned into the cylindrical shape with same radius. If the height of cylinder is 5 cm, the height of cone is :(A) 10 cm(B) 15 cm(C) 18 cm(D)24 cm
Answer» Answer is (B) 15 cm Let the common radius of the cone and cylinder be r. Let height of cone be h₁. And the height of cylinder h₂ = 5 cm. According to the problem Volume of cone = Volume of cylinder ⇒ \(\frac { 1 }{ 3 }\)πr²h₁ = πr²h₂ ⇒ \(\frac { { h }_{ 1 } }{ 3 }\) = h₂ = 5 ⇒ h₁ = 3 × 5 h₁ = 15 ∴ Height of cone = 15 cm

A metallic cone is turned into the cylindrical shape with same radius. If the height of cylinder is 5 cm, the height of cone is :(A) 10 cm(B) 15 cm(C) 18 cm(D)24 cm

Answer»

Answer is (B) 15 cm

Let the common radius of the cone and cylinder be r.

Let height of cone be h₁.

And the height of cylinder h₂ = 5 cm.

According to the problem

Volume of cone = Volume of cylinder

⇒ \(\frac { 1 }{ 3 }\)πr²h₁ = πr²h₂

⇒ \(\frac { { h }_{ 1 } }{ 3 }\) = h₂ = 5

⇒ h₁ = 3 × 5

h₁ = 15

∴ Height of cone = 15 cm