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Question
A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder (ii) left in the cylinder. (Take π 22/7)
Solution
We have a cylindrical vessel in which a cone is inserted. We have,
Radius of the cylinder(r1) = 5 cm
Radius of cone(r2) = 3.5 cm
Height of cylinder(h) = 10.5 cm
Height of cone(l) = 6 cm
(i) We have to find the volume of water displaced from the cylinder when cone is inserted.
So,
Volume of water displace = volume of cone
So volume of water displaced,
`=1/3pir_2^2l`
`=1/3(22/7)(12.25)(6) cm^3`
= 77 cm3
(ii) We have to find the volume of water remaining in the cylinder.
Volume of water left = Volume of cylinder - Volume of cone
So volume of the water left in the cylinder,
`=[(22/7(25)(10.5))-(77)] cm^3`
=(825-77)cm3
= 748 cm3
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