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A solid consisting of a right circular cone,standing on a hemisphere,is placed upright,in a right circular cylinder,full of water,and touches the bottom. Find the volume of water left in the cylinder,having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer correct to the nearest centimetre. (Take pie=3 1/7).
Let, height of cylinder be H and radius R; height of cone be h and radius of cone
and hemisphere be r
Volume of water left in the cylinder = [Volume of cylinder – (Volume of cone
+ Volume of hemisphere) ]
Or, V = [?R2H – {(1/3) ?r2h + (2/3) ?r3] cu.cm
Or, V = [?×32×6 – (1/3×?×22×4 + 2/3×?×23)] cu.cm
Or, V = [54? – (16?/3 + 16?/3)] cu.cm
Or, V = [54? – 32?/3] cu.cm
Or, V = (162? – 32?)/3 cu.cm
Or, V = (130/3)(22/7) cu.cm
Or, V = 136.cu.cm.


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