Question

Ugh I Need Help With This Problem Someone Help Me... Lol
Hester needs 14 square feet of material to make an inflatable ball. How much material to the whole foot would she need to make a ball with twice the diameter of the original?

Answer 1

ok... so find the radius...

using the surface area of a sphere

\[14 = 4\pi r^2\]

so the radius is

\[r = \sqrt{\frac{14}{4\pi}}\]

the radius of the larger ball will be

\[r = 2\sqrt{\frac{14}{4\pi}}\]

so the material can be found by using the surface area formula again

\[SA = 4\pi (2\sqrt{\frac{14}{4\pi}})^2\]

or

\[SA = 4\pi \times 4 \times \frac{14}{4\pi}\]


cancel som common factors and then multiply it out

Answer 2

So it would be SA = 4x 14/16 Pi ?

Answer 3

Or am i wrong ? & Thank you for your help !

Answer 4

Nvm I Got It

Answer 5

You do not need to work out the radius.

SA= 4pi r^2

if the new radius is 2r then the area = 4 pi (2r)^2 = 4pi *4(r^2)

You can easily see how many times bigger the area is than the original....