Question

In the equation SA = 4pier^2h, what happens to r if the height is tripled and the surface area remains the same?

Answer 1

As the surface area will remain constant, the equation yield to:\[4\pi r_{1}^{2}.h_1=4\pi r_{2}^{2}.h_2\]
and as the height is tripled, therefore \[h_2=3h_1\]
substitute and rearrange, we get:
\[r_{1}^{2}.h_1=r_{2}^{2}.h_2\]
\[r_{1}^{2}=3r_{2}^{2}\]
So the new radius will be 0.57735 times the old one.

Answer 2

So the new surface area is half?

Answer 3

You aren't asked about new surface area, you're asked about new radius.

New radius would be multiplied by \[\frac{ 1 }{ \sqrt 3 }\]or \[\frac{ \sqrt 3 }{3 }\]