The height of a cylinder is three times the diameter of the base. The surface area of the cylinder is 126pi sq ft. What is the radius of the base?

Question

tkhunny · Answer

Surface Area of Right Circular Cylinder is ...?

In terms of Height and Radius.

anonymous · Answer

Well. I know the formula is 
S.A. = L.A.+2B

anonymous · Answer

Where B is the area of the base.

tkhunny · Answer

Very good.  Now expand both "L.A." and "B" to be in terms of the Radius and Height.

anonymous · Answer

Would that be 2pi r h + 2pi r squared?

tkhunny · Answer

Super.  One more thing.  In the problem statement, we are told h = 3d = 2(3r) = 6r.  Do you see this?

anonymous · Answer

Yes

anonymous · Answer

Wait I think I get it!

tkhunny · Answer

Okay, we're ready to solve.  Write the rest of the problem statement.

tkhunny · Answer

See how sly you are?!  Now, solve directly for 'r'.  Perfect!

anonymous · Answer

I don't know if I'm doing my math right. I get something not in my choices, but it's closest to 3 ft. So that's what I put. Thank you so much!

tkhunny · Answer

126pi = 2pi r 6r + 2pi r squared

$2\pi r\cdot 6r + 2\pi r^{2} = 126\pi$

Divide by $\pi$

$2 r\cdot 6r + 2r^{2} = 126$

Simplify and divide by 2

$6r^{2} + r^{2} = 63$

Simplify

$7r^{2} = 63$

Divide by 7

$r^{2} = 9$

Look's like r = 3 is a good answer.  NOT r = -3.  That's not a good radius for a real cylinder.

anonymous · Answer

Did I say -3? But thank you again. I did do my math wrong.

tkhunny · Answer

No, you did not say "-3".

$r = -3$ IS a solution to $r^{2} = 9$, but it is not a solution to this problem.  Just trying to be thorough.