Watery

Geometry Level 3

Water runs into a cylindrical tank of height 100 cm 100\text{ cm} at the rate of 5 cm 3 /s 5\text{ cm}^3\text{/s} . If the radius of the base of this cylinder is 7 cm 7\text{ cm} , the find the rate of change of the water level in the tank.

The answer is of the form x y × π \dfrac{x}{y \times \pi} where x x and y y are coprime positive integers. Submit the value of x + y x + y .


The answer is 54.

Ashish Menon by Ashish Menon , 20, India

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1 solution

Abhay Tiwari
Apr 22, 2016

Volume of cylinder = π × r 2 × h \pi× r^{2}×h = 4900 π 4900\pi

Total time taken for the tank to get filled = 4900 π 5 = 980 π \frac{4900\pi}{5}=980\pi

Rate of change of water level= ( 100 − 0 ) c m 980 π s e c \frac{(100-0)cm}{980\pi sec}

= 5 49 π \frac{5}{49\pi}

Where x=5 & y=49 then x+y=54.

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