Question

The lateral surface area of a cylinder is equal to the curved surface area of a cone. If their bases be the same, find the ratio of the height of the cylinder to the slant height of the cone.

Answer 1

Answer:

1:2

Step-by-step explanation:

Lateral Surface Area of cylinder:

Radius = r.

Height = h.

Surface area = 2πrh

Curved Surface Area of cone:

Radius = r

Height = h

Surface Area = πrl

Given that their bases be the same.

2πrh = πrl

⇒ h/l = πr/2πr

⇒ h/l = 1/2

⇒ h : l = 1:2

Therefore, ratio of the height of the cylinder to the slant height = 1:2.

Hope it helps!

Answer 2

Step-by-step explanation:

lateral surface area of the cylinder = curved surface area of the cone (r is same )

1. 2*22/7 rh = 22/7*rl
2. 2h=l
3. h/l= 1/2
4. 1:2 ans