If the height of two riight circular Cylinders arein the ration 3:4 an

1.	If the height of two riight circular Cylinders arein the ration 3:4 and perimeters are in the ratio1:2 then find the ratio of their volumes.
Answer» Answer: RATIO of the height $= \frac{3h}{4h}$ i.e height of $cylinder_{1} = H = 3h$ height of $cylinder_{2} = H' = 4h$ ratio of the PERIMETER $= \frac{1p}{2p}$ e.i perimeter of $cylinder_{1} = 1p$ $2\pi rH = p$ $2\pi r(3h) = p$ $6\pi rh = p$ perimeter of $cylinder_{2} = 2p$ $2\pi r'H' = 2p$ $2\pi r'(4h) = 2p$ $8\pi r'h = 2p$ $=> \frac{6\pi rh }{8\pi r'h } = \frac{p}{2p}$ $=> \frac{6\pi rh }{8\pi r'h } = \frac{1}{2}$ $=> \frac{3r}{4r' } = \frac{1}{2}$ $=> \frac{r}{r' } = \frac{2}{3}$ ratio of the radius $= \frac{2R}{3R}$ i.e radius of $cylinder_{1} = 2R$ radius of $cylinder_{2} = 3R$ ratio of volume $= \frac{V_{1} }{V_{2} }$ i.e $V_{1} = \pi r^{2} H$ $= \pi (2R)^{2}(3h)$ $= 12\pi R^{2}h$ $V_{1} = \pi r'^{2} H'$ $= \pi (3R)^{2}(4h)$ $= 36 \pi R^{2}h$ Ratio of the volume $= \frac{ 12\pi R^{2}h}{36 \pi R^{2}h}$ $= \frac{ 12}{36}$ $= \frac{1}{3}$