# 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 = 4πr^{2}

The Curved surface area of the sphere = 4πr^{2}

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 (9r^{2}/16)

= (9πr^{2})/4

Now, decrease in the original curved surface area = 4πr - (9πr^{2})/4

= (16πr^{2}- 9πr^{2})/4

= (7πr^{2})/4

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

= [(7πr^{2})/4 × 1/(4πr^{2})] × 100%

= [7/16] × 100%

= 43.75%

**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%.