# If the radius of a sphere is increased by 2.5 decimetre (dm), then its surface area increases by 110 dm2. What is the volume (in dm3) of the sphere? (

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If the radius of a sphere is increased by 2.5 decimetre (dm), then its surface area increases by 110 dm2. What is the volume (in dm3) of the sphere?

(Take π = $\frac{22}{7}$)

1. $\frac{4}{7}$
2. $\frac{3}{7}$
3. $\frac{13}{21}$
4. $\frac{11}{21}$

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Correct Answer - Option 4 : $\frac{11}{21}$

Given:

The radius of a sphere is increased by 2.5 decimeter(dm),

then its surface area increases by 110 dm2

Concept used:

The surface area of sphere = 4πr2

The volume of sphere = (4/3) × πr3

Where r = radius and π = 22/7

a2 - b2 = (a + b)(a - b)

Calculation:

according to the question,

4π(r + 2.5)2 - 4πr2 = 110

⇒ 4π[(r + 2.5)2 - r2] = 110

⇒ 4π[(r + 2.5 + r)(r + 2.5 - r)] = 110

⇒ 4 × 22/7 × (2r + 2.5) × 2.5 = 110

⇒ 10 × (2r + 2.5) = 35

⇒ 20r + 25 = 35

⇒ r = 1/2 dm

now,

Volume = 4/3 × π × (1/2)3

⇒ 4/3 × 22/7 × 1/8

⇒ 88/168 = 11/21 dm3

∴ The volume of the sphere is 11/21 dm3.

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