Question

Diameter of a sphere is deereased by 25%o. What
is the deerease in percent in surface area of sphere.​

Answer 1

Answer:

Step-by-step explanation:

ANSWER

Original Diameter ==d

Original CSA=4\pi\left(\dfrac{d}{2}\right)^2=\pi d^2=4π(  

2

d

​  

)  

2

=πd  

2

 

New Diameter =d-\dfrac{25}{100}d=\dfrac{3d}{4}=d−  

100

25

​  

d=  

4

3d

​  

 

New CSA=4\pi \left(\dfrac{3d}{8}\right)^2=\dfrac{9}{16}\pi d^2=4π(  

8

3d

​  

)  

2

=  

16

9

​  

πd  

2

.

\%% decrease =\dfrac{(\pi d^2-\dfrac{9}{16}\pi d^2)}{\pi d^2}\times 100=  

πd  

2

 

(πd  

2

−  

16

9

​  

πd  

2

)

​  

×100

=\dfrac{\pi d^2}{\pi d^2}\left(1-\dfrac{9}{16}\right)\times 100=  

πd  

2

 

πd  

2

 

​  

(1−  

16

9

​  

)×100

=\dfrac{16-9}{16}\times 100=  

16

16−9

​  

×100

=43.75\%=43.75%