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medium difficulty5 min

Surface area of a sphere

The surface area of a sphere is the total area of its outer curved surface.

In one line: Sphere surface is four times the circle area.

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Understand it

A sphere has no flat base or edges. Every point on the surface is equally distant from the center, so the entire outside is one smooth curved surface. Because there is no separate base, the formula is simply based on the radius alone.

Example

A sphere of radius 6 cm has surface area 4πr² = 4π × 36 = 144π cm², which is 452.57 cm² approximately.

Formula and rule

Surface area of a sphere = 4πr², where r is the radius of the sphere.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For r = 6 cm, surface area = 4πr² = 4 × π × 36 = 144π cm².

Method you can reuse

  1. 1Read the radius.
  2. 2Square it first.
  3. 3Multiply by 4π.
  4. 4Simplify the value.
  5. 5Write the answer in square units.

Sketch it in your answer

Draw a circle to represent the sphere in a sectional view and mark the radius from the center to the surface. Stress that the entire outside is curved.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A solid ball is to be wrapped completely. Which formula gives its surface area?

Think first, then show answer
Use 4πr², because a sphere has only one curved outer surface and no flat base.

Common wrong answer

A common wrong answer is 2πr². That is only half of the sphere formula and gives an incorrect surface area.

Don't mix this up

Students often use 2πr² or treat the sphere like a hemisphere or cylinder.

Exam tip

For any sphere, remember that only the radius is needed: 4πr².

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Find the wrapping area of a ball, marble, solid sphere, or globe using the given radius.
  1. 1

    Enough for 1 mark

    The surface area of a sphere is the total area of its outer curved surface.

  2. 2

    Add for 2 marks

    Example: A sphere of radius 6 cm has surface area 4πr² = 4π × 36 = 144π cm², which is 452.57 cm² approximately.

  3. 3

    Add for 3 marks

    A sphere has no flat base or edges.

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