Question

PLEASE HELP?

Suppose the sphere below with radius r has a surface area equal to 50 units². find the surface area of the sphere with twice the radius.

Answer 1

`200$ unit^2`

Explanation:

Surface Area of a Sphere
`=4\pi r^2`

Given that the surface area of a sphere is 50 units².

Then:

`4\pi r^2 =50\\r^2=(50)/(4\pi)\\ r=\sqrt{(50)/(4\pi)}`

If a sphere has twice the radius of the sphere above

Its radius,
`r=2\sqrt{(50)/(4\pi)}`

Therefore its Surface Area

`=4\pi\left(2\sqrt{(50)/(4\pi)}\right)^2\\=4\pi*4*(50)/(4\pi)}\\\\=200 unit^2`