tank is . × litres. If the diameter of the tank is m, find its height. Solution Let r and h be the radius and height of the cylinder respectively.
Given that, volume of the tank = = 1078000 litre = m ( l = m ) diameter = m Þ radius = m volume of the tank = p r h cu. units = h Therefore, height of the tank is m h Fig. . R Example .
Find the volume of the iron used to make a hollow cylinder of height cm and whose internal and external radii are cm and cm respectively. Solution Let r, R and h be the internal radius, external radius and height of the hollow cylinder respectively. Given that, r = cm, R = cm, h = cm Now, volume of hollow cylinder = p ( R r h cu. units ) × ) × = Therefore, volume of iron used = cm Example .
For the cylinders A and B (Fig. . ), (i) find out the cylinder whose volume is greater. (ii) verify whether the cylinder with greater volume has greater total surface area.
(iii) find the ratios of the volumes of the cylinders A and B . Solution (i) Volume of cylinder = p r h cu. units Volume of cylinder A = = . cm Volume of cylinder B = = .
cm Therefore, volume of cylinder B is greater than volume of cylinder A . (ii) T.S.A. of cylinder = p r h ) sq. units T.S.A.
of cylinder A = . ) = cm T.S.A. of cylinder B = . ) = cm Hence