An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 7 cm, and the height is 10 cm. find the rate at which the water level is rising when the water level is 4 cm.

Rate of change in height of the water level is 2.91 cm per second.

Step-by-step explanation:

Height of the inverted pyramid = 10 cm

Length of the square base = 7 cm

If water is filled up to the level of h cm then the volume of water up to height h will be

V =

V =

It is given that rate of water is filling with 70 cubic centimeters per second.

From two similar triangles in the figure attached,

By replacing the value of h,

V =

V =

V =

Now we integrate the equation with respect to time 't'

70 =

For h = 7 cm

Therefore, rate of change in height of the water level is 2.91 cm per second.

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step-by-step explanation: