Question

if volume are in ratio of 64:27 thant ratio of surface area is equal to​

Answer 1

Answer:

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Step-by-step explanation:

Let the radius of two spheres be

r_(1)

and

r_(2)

<br> Given, the ratio of the volume of two spheres = 64: 27 <br>

(V_(1))/(V_(2)) =(64)/(27) rArr ((4)/(3)pir_(1)^(3))/((4)/(3)pir_(2)^(3)) = (64)/(27)

<br>

rArr" "((r_(1))/(r_(2)))^(3) = ((4)/(3))^(3) " "[because "volume of sphere" =(4)/(3) pir^(3)]

<br>

rArr " "(r_(1))/(r_(2)) =(4)/(3)

<br> Let the surface areas of the two spheres

S_(1)

and

S_(2)

<br>

therefore" "(S_(1))/(S_(2)) = (4pir_(1)^(2))/( 4pir_(2)^(2)) = ((r_(1))/(r_(2)))^(2) rArr S_(1),S_(2) = ((4)/(3))^(2) = (16)/(9)

<br>

rArr" "S_(1),S_(2) = 16:9

<br> Hence, the ratio of the their surface areas is 16: 9.

Answer 2

Volume of sphere=  

3

4

​

πr  

3

 

Then,

Volumeofsphere(2)

Volumeofsphere(1)

​

=  

27

64

​

 

3

4

​

πr  

2

​

 

3

 

3

4

​

πr  

1

​

 

3

 

​

=  

27

64

​

 

r  

2

​

 

3

 

r  

1

​

 

3

 

​

=  

27

64

​

 

r  

2

​

 

r  

1

​

 

​

=  

3

4

​

 

Then, Ratio of areas both spheres

areaofsphere(2)

areaofsphere(1)

​

=  

4πr  

2

​

 

2

 

4πr  

1

​

 

2

 

​

 

=  

r  

2

​

 

2

 

r  

1

​

 

2

 

​

 

=(  

r  

2

​

 

r  

1

​

 

​

)  

2

 

=(  

3

4

​

)  

2

 

=  

9

16

​

 

Hence, this is the answer.