Question

There are two ice cream cone the curved surface area of first one if twice that of the second one the slant heighth of the second cone is twice that of first cone find the ratio of there heights

Answer 1

Let radii of the cones be r1 ,r2 and slant height of the cones l1 and l2.

According to the question = πr1l1 = 2πr2l2

⇒ r1 l1 = 2r2 l2 -------(1)

Given that slant height of the second cone is twice the first cone i.e

⇒ l2 = 2 l1 ----------(2)

From (1) and (2) we get

r1 l1 = 2r2 2l1

⇒ r1 = 4r2

⇒ r1 / r2 = 4 / 1.

∴ Ratio of radii = 4:1.

Answer 2

Let radii of the cones be r1 ,r2 and slant height of the cones l1 and l2.

According to the question = πr1l1 = 2πr2l2

⇒ r1 l1 = 2r2 l2 -------(1)

Given that slant height of the second cone is twice the first cone i.e

 ⇒ l2 = 2 l1 ----------(2)

From (1) and (2) we get

 r1 l1 = 2r2 2l1

⇒ r1 = 4r2 

⇒ r1 / r2  = 4 / 1.

∴ Ratio of radii = 4:1.