Question

# A conical empty vessel is to be filled up completely by pouring water into it successively with the help of a cylindrical can of diameter 6 cm and height 12 cm. The radius of the conical vessel is 9 cm and its height is 72 cm. How many times will it require to pour water into the conical vessel to fill it completely, if in each time the cylindrical can is filled with water completely?

A
14
B
18
C
20
D
12

Solution

## The correct option is B 18Let $$n$$ be the required number of times. Then, the volume of the conical vessel will be equal to the volume of the cylindrical can.Now, the volume of the conical vessel$$=\dfrac {1}{3}\pi \times 9^2\times 72 cm^3=24\times 81\pi cm^3$$And the volume of the cylindrical cane$$=\pi \times 3^2\times 12 cm^2=9\times 12 \pi cm^3$$Hence, $$24\times 81\pi =9\times 12 \pi \times n$$$$\Rightarrow n=\dfrac {24\times 81}{9\times 12}=18$$Hence, the required number of times $$=18$$.Mathematics

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