Question

The diameter of a sphere is decreased by 20 percent by what percent does its total surface area decrease​

Answer 1

Step-by-step explanation:

Answer

Let the diameter of sphere be "d"

curved surface area of sphere =4πr

2

=π(2r)

2

=πd

2

Given diameter of sphere decreases by 20%

New diameter =d−(

5

d

)=

5

4d

New curved surface area =π(

5

4d

)

2

=(

25

16

)πd

2

Change in surface area of sphere =πd

2

–(

25

16

)πd

2

=(

25

9

)πd

2

decrease in curved surface area =

⎣

⎢

⎢

⎡

πd

2

25

9

πd

2

⎦

⎥

⎥

⎤

×100=36%

∴ surface area decreases by 36 percent