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ICSE Class 10 Mathematics Question 2 of 21

Solved 2025 Specimen Paper ICSE Class 10 Mathematics — Question 6

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6
Question

Question 1(vi)

A solid sphere is cut into identical hemispheres.

Statement 1 : The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2 : The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid ?

  1. Both the statements are true

  2. Both the statements are false

  3. Statement 1 is true, and statement 2 is false

  4. Statement 1 is false, and statement 2 is true

Answer

When a solid sphere is cut into identical hemispheres.

Let radius of sphere be r.

Volume of a sphere = 43πr3\dfrac{4}{3}πr^3

Volume of hemisphere = 23πr3\dfrac{2}{3}πr^3

Volume of 2 hemisphere = 2×23πr3=43πr32 \times \dfrac{2}{3}πr^3 = \dfrac{4}{3}πr^3.

The total volume of two hemispheres is equal to the volume of the original sphere.

Surface area of sphere = 4πr2

Surface area of hemisphere = 3πr2

Surface area of 2 hemisphere = 2 × 3πr2 = 6πr2.

The surface area of two hemispheres is not equal to the surface area of the original sphere.

Hence, Option 3 is the correct option.