Question
Water flows at the rate of 10 metres per minutes from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?
Answer: Option B
Volume flown in conical vessel :
$$\eqalign{
& = \frac{1}{2}\pi \times {\left( {20} \right)^2} \times 24 \cr
& = 3200\pi \cr} $$
Volume flown in 1 minute :
$$\eqalign{
& = \left( {\pi \times \frac{{2.5}}{{10}} \times \frac{{2.5}}{{10}} \times 1000} \right) \cr
& = 62.5\pi \cr} $$
∴ Time taken :
$$\eqalign{
& = \left( {\frac{{3200\pi }}{{62.5\pi }}} \right) \cr
& = 51\operatorname{minutes} 12\operatorname{seconds} \cr} $$
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Volume flown in conical vessel :
$$\eqalign{
& = \frac{1}{2}\pi \times {\left( {20} \right)^2} \times 24 \cr
& = 3200\pi \cr} $$
Volume flown in 1 minute :
$$\eqalign{
& = \left( {\pi \times \frac{{2.5}}{{10}} \times \frac{{2.5}}{{10}} \times 1000} \right) \cr
& = 62.5\pi \cr} $$
∴ Time taken :
$$\eqalign{
& = \left( {\frac{{3200\pi }}{{62.5\pi }}} \right) \cr
& = 51\operatorname{minutes} 12\operatorname{seconds} \cr} $$
Was this answer helpful ?
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