Question

Surface area of a sphere is 4pir^2. If the radius of a sphere is doubled, by what factor would the surface area be enlarged?

Answer 1

Answer :-

Given :-

• Radius of a sphere is doubled

To Find :-

• By what factor would the surface area of sphere be enlarged.

Solution :-

We know that,

→ Surface area of sphere = 4πr²

Here, it is given that radius is doubled. So, we can substitue r by 2r.

→ New surface area = 4 × π × (2r)²

→ New surface area = 4 × π × 4r²

→ New surface area = 16πr²

16πr² = 4 ( 4πr² )

New surface area = 4 ( surface area )

So, the surface area is increased by 4 times.

Answer 2

S.A. = 4πr²

New radius (r') = 2r

New S.A. = 4πr'²

= 4π(2r)²

=4π ×4r²

= 4 × 4πr²

this implies that 4 is the factor by which surface area is enlarged