The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

Solution:

Given: diameter of a sphere is decreased by 25%.

We have to find the percentage by which its Curved Surface Area decreases.

Let the radius of the sphere be r.

Then its diameter is 2r.

The Surface area of a sphere = 4πr²

The Curved surface area of the sphere = 4πr²

Now it is given in the question that the diameter of the sphere is decreased by 25% hence a new sphere is formed.

Therefore, the diameter of the new sphere can be written as:

= 2r - (25%) of (2r)

= 2r - (25/100) × (2r)

= 2r - (r/2)

= 3r/2

Radius of the new sphere = 1/2 × 3r/2 = 3r/4

Hence, curved surface area of the new sphere = 4π (3r/4)²

= 4π (9r²/16)

= (9πr²)/4

Now, decrease in the original curved surface area = 4πr - (9πr²)/4

= (16πr²- 9πr²)/4

= (7πr²)/4

So, the percentage decrease in the curved surface area is,

= [(7πr²)/4 × 1/(4πr²)] × 100%

=  [7/16] × 100%

= 43.75%

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

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Video Solution:

The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.9 Question 3

Summary:

It is given that the diameter of a sphere is decreased by 25%. We have found that the original curved surface area decreases by 43.75%.

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