Question

The diameter of a sphere is decreased by 30%. By what percent its surface area decreases.

Answer 1

Given :-

• Diameter of Sphere is Decreased by = 30% .

To Find :-

• By what percent its surface area decreases. ?

Formula used :-

• TSA of Sphere = 4 * π * (radius)² .
• Radius = (Diameter) / 2 .

Solution :-

Let us Assume That, initial Diameter of Sphere is 20cm.

So,

→ Radius of Sphere = (20/2) = 10cm.

→ TSA of initial Sphere = 4 * π * (10)² = 400π cm². ------ Equation (1).

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Now, diameter of a sphere is decreased by 30%.

So,

→ New Diameter = 20 - (30% of 20) = 20 - [ (30*20)/100 ] = 20 - 6 = 14cm.

→ New Radius = 7 cm.

→ TSA of New Sphere = 4 * π * (7)² = 196π cm². ------ Equation (2).

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From Equation (1) & (2) Now, we get,

→ Decreased in Surface Area = 400π - 196π = 204π cm².

Hence,

→ % Decreased = (204 π * 100) / 400π = 51% . (Ans.)