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The Diameter of a Sphere is Decreased by 25%. by What per Cent Does Its Curved Surface Area Decrease? - Mathematics

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

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Solution

Let the diameter of the sphere be d.

Radius (r1) of sphere = d/2

New radius (r2) of sphere `= d/2(1-25/100)=3/8d`

CSA (S1) of sphere `= 4pir_1^2`

`=4pi(d/2)^2=pid^2`

CSA (S2) of sphere when radius is decreased`= 4pir_2^2`

`=4pi((3d)/8)^2=9/16pid^2`

Decrease in surface area of sphere = S1 − S2

`=pid^2-9/16pid^2`

`=7/16pid^2`

`"Percentage decrease in surface area of sphere "=(S_1-S_2)/S_1xx100`

                                                                       `= (7pid^2)/(16pid^2)xx100=700/16=43.75%`

Concept: Volume of a Sphere
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APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.9 | Q 3 | Page 237

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