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Question
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
Solution
For a large cylindrical vessel,
Height = H = 24 cm
Radius = R = `40/2` = 20 cm
∴ Volume of large cylindrical vessel = πR2H
= (π × 20 × 20 × 24) cm3
For each small cylindrical bottle,
Height = h = 10 cm
Radius = r = `8/2` = 4 cm
∴ Volume of each small cylindrical bottle = πr2h
= (π × 4 × 4 × 10) cm3
Now, number of small cylindrical bottles which can filled
= `"Volume of large cylindrival vessel"/"Volume of each small cylindrical bottle"`
= `(pi xx 20 xx 20 xx 24)/(pi xx 4 xx 4 xx 10)`
= 60
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