Question

The diameter of a sphere is decreased by 25%. By what per cent does it’s curved surface area decrease?​

Answer 1

Answer:

43.75%

Step-by-step explanation:

Let the original diameter of the sphere be 2x.

Then, original radius of the sphere = x

Original curved surface area = 4πr2

Decreased diameter of the sphere = 2x - 25% of 2x = 2x - x/2 = 3/2x

Decreased radius of the sphere = 3/4x

∴ Decreased curved surface area = 4π(3/4.x)2 = 9/4πx2

Decrease in area = 4πx2 - 9/4πx2 = 7/4πx2

Hence, percentage decreases in area = 7/4πx2/4πx2 x 100% = 7/16 x 100% = 175/4%

= 43.75%

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Answer 2

Answer:

CSA decreases by 43.75%.

Explanation:

If we reduce the diameter by 25%, the radius will also be reduced by 25%.

let the initial radius of sphere = r

initial CSA = 4πr²

after reducing it 25%,

25% of r = (25/100)×r = 0.25r

final radius = r - 0.25r = 0.75r

final CSA = 4π(0.75r²) = 4πr²×(0.5625)

decrease in CSA = initial CSA - final CSA = 4πr² -  4πr² × (0.5625)

⇒decrease in CSA = 4πr² × (1-0.5625) = 4πr² × 0.4375

% decrease in CSA =  

Thus CSA decreases by 43.75%.

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