In a cylindrical tank, rice is increasing at a rate of ` 314 m^(3)//hr`. Find the rate of increase of the height of the rice in cylindrical tank when the radius of the base of tank is 5 m.

Options

A. `1 m//hr`
B. `2 m//hr`
C. `3 m//hr`
D. `4 m//hr`

Answer

D

Explanation

Let 'r' be the radius of the tank and at any time 't' the height of the rice be 'h'.
Give that r = 5 m
Volume of rice in tank
`v=pi r^(2)h`
` = pi (5)^(2)h" " (.:' "r is constant" )`
`= 25 pi h`
`rArr (dV)/(dt)= 25pi.d/(dt)(h)=25pi.(dh)/(dt)`
`rArr 314 = 25 xx 3 . 14 xx (dh)/(dt)`
`rArr (dh)/(dt) = 4 m//hr`
Therefore height of rice in the tank is increasing at a rate of 4 m/hr.