SOLUTION: The dimensions of a cylinder, its radius and height are each doubled. What is true about its resulting surface area? a) The resulting volume is double the original surface area.

Question 287853: The dimensions of a cylinder, its radius and height are each doubled. What is true about its resulting surface area?
a) The resulting volume is double the original surface area.
b) The resulting volume is triple the original surface area.
c) The resulting volume is 4 times the original surface area.
d) The resulting volume is 6 times the original surface area.
e) The resulting volume is 8 times the original surface area.
Found 2 solutions by Grinnell, dabanfield:
Answer by Grinnell(63) (Show Source):
You can put this solution on YOUR website!
The answer is E.
When doing these try to KEEP IT SIMPLE.
We are concerned with ratios--not actual measures.
Sooo WHY NOT let the original radius and height be ONE?????
pi (r^2)height = pi or, pi TIMES 1 TIMES 1=======just little ole' pi.
NOW we double--let r be two and so H is 2 also.
NOW we get pi(4)(2)=8(pi) so
pi/8pi is the relationship, you are left with 8pi! (The pi's cancel out!)

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
Let h be the original height and r the original radius. The the surface area (two ends and side) is:
2*(pi*r^2) + (2*r*pi)*h (note that 2*r*pi is the circumference of the cylinder).
If we double the height and the radius the surface area becomes:
2*(pi*(2*r)^2) + (2*(2*r)*pi)*h =
2*4*r^2*pi + 2*2*r*pi*h =
4*2*(pi*r^2) + 2*(2*r*pi)*h

The original volume is (pi*r^2)*h.
The new volume is (pi*(2r)^2*(2*h)=
pi*4*r^2*2*h = 8*((pi*r^2)*h)