Question

The surface areas of a sphere and a cube are equal. Find the ratio of the volumes of the sphere and the cube. Take pi as 22/7​

Answer 1

Answer:

Step-by-step explanation:

Surface Area of a cube =6a2

Surface Area of a sphere =4πr2

We are given,

4πr2=6a2

⇒

r

a

 

=

√

3

2π

 

Now, ratio of their volume,

Volume of sphere/Volume of cube =  

4

3

 

πr3

a3

 

=

4

3

 

π(

r

a

 

)3=

4

3

 

π(

3

2π

 

)∗

√

3

2π

 

=2

√

3

2π

 

=

√

4∗3∗7

2∗22

 

=

√

21

11

 

So, required ratio is  

√

21

11

 

.

Answer 2

Step-by-step explanation:

take pi=22/7] So, required ratio is √2111.