Mathematics: 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?

A cylindrical tank with radius 3m is being filled

marvezunderwood

16.03.2022

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 :

$V = \pi r^2h$ ....1)

Also, we have given that, $\dfrac{dV}{dt} = 4 \ m^3/min$ .

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

$\dfrac{dV}{dt} =3^2 \pi \dfrac{ dh }{dt}\\\\\dfrac{dh}{dt} = \dfrac{4}{3^2 \times \pi}\\\\\dfrac{dh}{dt} = 0.141 \ m/min$

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

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izzzzz49

24.08.2021

9. slope: 1/2 y-int: -4

10. y=20x+50

11. y=-40x+300

12. i dnt know

13.9/6+3/6x=y or 1.5+0.5=y

Step-by-step explanation:

10. starts at 50, goes up by 20 per week

11. starts at 300, goes down 40 per week

13.

9+3x=6y

9/6+3/6x=y or 1.5+0.5=y

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