Study Guides/Maths/Curved Surface Area of a Cone
Study Guide · Maths

Curved Surface Area (CSA) of a Cone Formula

A right circular cone has two surfaces: the flat circular base and the curved wall. The Curved Surface Area (CSA) refers ONLY to the area of the curved wall, excluding the base.

Question (Click to Flip)

What is the formula for the curved surface area of a cone?

Answer

The formula for the curved surface area of a cone is πrl, where 'r' is the radius and 'l' is the slant height.

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Key Facts

CSA of Cone: πrl.

TSA of Cone: πr(l + r).

Slant height formula: l = √(r² + h²).

CSA does NOT include the bottom flat circle.

The Formula

CSA of a Cone = πrl

Where:

  • π (pi) = 22/7 or 3.14
  • r = Radius of the circular base
  • l = Slant height of the cone

How to find Slant Height (l)?

Often, exam problems give you the straight height (h) instead of the slant height (l). You must use Pythagoras theorem to find 'l' first:

l² = r² + h² l = √(r² + h²)

Total Surface Area (TSA)

If you need the Total Surface Area, you add the area of the circular base (πr²) to the CSA: TSA = πrl + πr² TSA = πr(l + r)

Questions and Answers

What is the formula for the curved surface area of a cone?+

The formula for the curved surface area of a cone is πrl, where 'r' is the radius and 'l' is the slant height.

How do you find the slant height of a cone?+

The slant height (l) is found using the Pythagorean theorem: l = √(r² + h²), where r is radius and h is straight height.

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