Two spheres have a volume ratio of 64 : 27. If the sum of their radii is 7 cm, then the difference in their surface areas is ____

c
m
2

.

Question

Two spheres have a volume ratio of 64 : 27. If the sum of their radii is 7 cm, then the difference in their surface areas is ____

c
    m
    2
   
   .

Accepted Answer

Two spheres have a volume ratio of 64 : 27. If the sum of their radii is 7 cm, then the difference in their surface areas is

88 c
    m
    2
   
   .
   It is given that the volume of two spheres is in the ratio of 64 : 27 and the sum of their radii is 7 cm.We know that the volume of a sphere is

4
    3
   
   π
    r
    3

and its surface area is

4π
    r
    2
   
   ,
   where r is the sphere’s sphere.Let’s assume that the radius of one sphere is

r cm.
   Therefore from the question, we have,The radius of another sphere is

7−r
    cm.
  The ratio of their volumes is 64 : 27.

∴

4
        3
       
       π
        r
        3

4
        3
       
       π

7−r
         
        3

=
      
       64
      
       27

⇒

r
         
          7−r

3
     
     =

4
         3

3

⇒
      r
      
       7−r
     
     =
      4
      3

⇒3r=28−4r

⇒7r=28

⇒r=4 cm

Therefore, the radius of one sphere is

4 cm.
   The radius of another sphere is

7−4
    cm = 3 cm.
  Therefore the difference in their surface areas can be calculated as,

∴D=4π
      
       4
      
      2
     
     −4π
      
       3
      
      2

⇒D=4π
      
       16−9

⇒D=4×
      
       22
      7
     
     ×7

⇒D=88
       cm
      2

Therefore, the difference in their surface areas is

88 
    
     cm
    2
   
   .

Two spheres have a volume ratio of 64 : 27. If the sum of their radii is 7 cm, then the difference in their surface areas is ____ $c m 2 .$

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

Two spheres have a volume ratio of 64 : 27. If the sum of their radii is 7 cm, then the difference in their surface areas is ____ c m 2 .