Question

The surface area of a sphere is π sq.cm.If it's radius is doubled,by how much does its surface area increase?​

Answer 1

Doubling the radius of a sphere will increase its surface area 4 times

Explanation:

The surface area of a sphere with radius r is given by the formula:

`SA = 4\pi r^2`

Doubling the radius means: r=> 2r

Putting the new radius the new surface area will be:

`SA_1 = 4\pi (2r)^2\\SA_1 = 4\pi (4r^2)\\SA_1 = 4(4\pi r^2)\\SA_1 = 4(SA)`

The new surface area with double radius is 4 times of the old surface area with r.

Hence,

Doubling the radius of a sphere will increase its surface area 4 times