A cylindrical tank with radius 3m is being filled with water at a rate 4m^³/min. How fast is the height of the water increasin?

Given :

A cylindrical tank with radius 3m is being filled with water at a rate 4m³/min.

To Find :

How fast is the height of the water increasing.

Solution :

We know, volume of cylinder is given by :

      ....1)

Also, we have given that, .

Differentiating equation 1) w.r.t  t we get :

Therefore, the height of water is increasing at a rate of 0.141 m/min.

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step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.