Study Guides/Maths/TSA of Hemisphere
Study Guide · Maths

Total Surface Area of Hemisphere – Formula and Derivation

A hemisphere is exactly half of a sphere. In Class 9 and 10 Mensuration, you need to know two important surface area formulas for a hemisphere.

Question (Click to Flip)

What is the formula for the total surface area of a hemisphere?

Answer

TSA of hemisphere = 3πr², where r is the radius.

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Key Facts

CSA of Hemisphere: 2πr².

TSA of Hemisphere: 3πr².

Volume of Hemisphere: (2/3)πr³.

The extra πr² in TSA comes from the flat circular bottom face.

The Two Formulas

Let r = radius of the hemisphere.

  1. Curved Surface Area (CSA) = Half the surface area of a sphere = 2πr² (Only the curved dome part, not the flat circular base.)

  2. Total Surface Area (TSA) = Curved Surface Area + Area of circular base = 2πr² + πr² = 3πr²

Solved Example

Find the TSA of a hemisphere with radius = 7 cm. TSA = 3πr² = 3 × (22/7) × 7 × 7 = 3 × 22 × 7 = 462 cm²

CSA = 2πr² = 2 × (22/7) × 7 × 7 = 308 cm²

Volume of Hemisphere

Volume = (2/3)πr³

Questions and Answers

What is the formula for the total surface area of a hemisphere?+

TSA of hemisphere = 3πr², where r is the radius.

What is the difference between CSA and TSA of a hemisphere?+

CSA (2πr²) includes only the curved dome surface. TSA (3πr²) includes the dome plus the flat circular base (πr²).

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