Answer:
Volume of the larger one = 476.5625
Step-by-step explanation:
Remark
This is a terrific little problem. Thanks for posting. I hope the answer is still useful to you. If the cylinders are similar it means that r and h are multiplied by a constant when moving from the smaller cylinder to the larger one. Everything else, believe it or not, remains the same.
Equations
Surface area of the smaller cylinder = 2pi*r^2 + 2pi*r*h
Surface area of the larger cylinder = 2*pi*(kr)^2 + 2pi*(kr)*(kh)
Surface area of the larger cylinder = k^2 (2*pi*r^2 + 2pi* r*h)
Solution
Surface area of the larger cylinder = k^2 (2pi*r^2 + 2pi*r*h)
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Surface area of the smaller cylinder (2pi*r^2 + 2pi*r*h)
surface area of the larger cylinder = k^2
surface are of the smaller cylinder = 1
200 / 128 = k^2 / 1 Divide the top and bottom of the left by 8
25 / 16 = k^2 Take the square roots of both sides
sqrt(25/16) = sqrt(k^2)
5/4 = k
Now work on the volume.
The volume of the larger cylinder = pi (kr)^2 (kh) = k^3 * pi * r^2 h
The volume of the smaller cylinder = pi * r^2 h
The volume of the larger cylinder to the smaller one = k^3 = 1.953125
x / 244 = 1.953125 Multiply both sides by 244
x = 1.953125 * 244
x = 476.5625
