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Question
A solid piece of wooden cone is of radius OP = 7 cm and height OQ = 12 cm. A cylinder whose radius and height equal to half of that of the cone is drilled out from this piece of wooden cone. Find the volume of the remaining piece of wood. (Use, `pi = 22/7`)
Solution
Cons -
OP (r) = 7 cm
OQ (h) = 12 cm
Cylinders -
r' = `7/2` cm
h' = `12/2` = 6 cm
Volume = Volume of Cone - Volume of cylinder
`= 1/3 pi"r"^2"h" - pi"r'"^2 "h'"^2`
`= 1/3 xx pi xx 7 xx 7 xx 12 - pi xx 7/2 xx 7/2 xx 6`
`= pi xx 7 xx 7 {1/(cancel3) xx cancel(12)^4 - 1/cancel(2) xx 1/2 xx (cancel(6)^3}`
`= 22/7 xx 7 xx 7 xx {4 - 1.5}`
= 22 × 7 × 2.5
= 385 cm3
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