Question

The diameter of one sphere is double the diameter of another.If the numerical value of total surface area of larger sphere is equal to the volume of smaller sphere, then find the radius of smaller sphere.​

Answer 1

Step-by-step explanation:

ANSWER

Let S

1

be the original surface area of the sphere and S

2

be the surface area with double the diameter.

Doubling the diameter means doubling the radius. Let r

1

and r

2

corresponding radii.

We know that S=4πr

2

and r

2

=2r

1

....Given

Hence,

S

2

S

1

=

4πr

2

2

4πr

1

2

⇒

S

2

S

1

=

(2r

1

)

2

r

1

2

⇒S

2

=4S

1

so, in complying with the question above we can say that x is equivalent to 4

So, doubling radius will increase S by a factor of 4.