Question

Curved surface area of a cone is 60 square centimetres. What is the curved surface area of another cone with same radius but slant height is one third of this cone ?

• A. 45 square centimetres
• B. 60 square centimetres
• C. 30 square centimetres
• D. 20 square centimetres

Hint:

The CSA of a cone is directly proportional to its slant height (CSA l) when the radius is constant. If the slant height becomes (1)/(3) of the original, the CSA will also become (1)/(3) of the original area. So, simply calculate (1)/(3) × 60 = 20.

Answer 1

The Correct Option is D

We are given the curved surface area (CSA) of a cone. We need to find the CSA of a new cone which has the same radius but its slant height is one-third of the original cone's slant height.

The formula for the Curved Surface Area (CSA) of a cone is given by:
CSA = π r l where r is the radius of the base and l is the slant height.

Let the original cone have radius r and slant height l.
Given, the CSA of the original cone is 60 square centimetres.
CSAₑₓtₒᵣᵢgᵢₙₐl = π r l = 60 cm² Now, consider the new cone.
The radius of the new cone is the same, r' = r.
The slant height of the new cone is one-third of the original slant height, l' = (1)/(3)l.
The CSA of the new cone will be:
CSAₑₓtₙₑw = π r' l' Substituting the new values:
CSAₑₓtₙₑw = π (r) ((1)/(3)l) CSAₑₓtₙₑw = (1)/(3) (π r l) Since we know that π r l = 60, we can substitute this value:
CSAₑₓtₙₑw = (1)/(3) × 60 CSAₑₓtₙₑw = 20 cm² The curved surface area of the new cone is 20 square centimetres.
(Note: The checkmark in the provided image is on (c) 30, which would be correct if the slant height was halved. Based on the question text "one third", the correct answer is 20.)