Question

if the radius of a sphere is double what will happen to its surface area

Answer 1

Surface area of sphere=4πr²

Let the initial radius be R
SA=4πR²

Now when the radius is doubled:
new SA=4π(2R)² = 4× 4πR²
new SA= 4× 4πR²
            = 4× (old SA)         [because 4πR²=old SA ]
           =4 × SA

So the new surface area will increase by 4 times.

Answer 2

let the radius of the sphere be r

original surface area = 4 x pi x r^2

new radius = 2r

surface area
= 4 x pi (2r)^2
= 4 x pi x 4 r^2

now

surface area of original sphere/ surface area of new sphere

= (4 x pi x r^2) / (4 x pi x 4r^2)
=1/4

therefore

surface area of new sphere
= 4( surface area of original sphere)