The ratio of the lateral surface areas of two right cylinders is 25/144. The volume of the first cylinder is 125 cm3 while the volume of the second cylinder is 1700 cm3. Are the two cylinders similar? Explain your answer.
-
The lateral surface area of a cylinder is 2*pi*r*h and the volume is pi*r^2*h. In this case we have
A1 / A2 = (2*pi*r1*h1)/(2*pi*r2*h2) = (r1*h1)/(r2*h2) = 25/144 and
V1 / V2 = (pi*r1^2*h1)/(pi*r2^2*h2)= (r1^2*h1)/(r2^2*h2) = 125/1700. Divide the second ratio by the first and simplify to find that r1 / r2 = (125/1700)/(25/144) = 720/1700. For the cylinders to be similar the ratio between h1 and h2 should be the same; check this on the area ratio ==> (720/1700)(720/1700) =
25.8 / 144, which means the cylinders are close to being similar, although not exactly. Doing the same thing with the volume ratio yields a ratio of 129 / 1700, again close but not exact.
A1 / A2 = (2*pi*r1*h1)/(2*pi*r2*h2) = (r1*h1)/(r2*h2) = 25/144 and
V1 / V2 = (pi*r1^2*h1)/(pi*r2^2*h2)= (r1^2*h1)/(r2^2*h2) = 125/1700. Divide the second ratio by the first and simplify to find that r1 / r2 = (125/1700)/(25/144) = 720/1700. For the cylinders to be similar the ratio between h1 and h2 should be the same; check this on the area ratio ==> (720/1700)(720/1700) =
25.8 / 144, which means the cylinders are close to being similar, although not exactly. Doing the same thing with the volume ratio yields a ratio of 129 / 1700, again close but not exact.