A receptacle is in the shape of an inverted square pyramid 10 inches in height and with a 6 x 6 square base. The volume of such a pyramid is given by

(1/3) (area of the base) (height)

Suppose that the receptacle is being filled with water at the rate of. 2 cubic inches per second. How fast is water rising when it is 2 inches deep?

Question

Mathematics

Sophia Hess

24 June, 02:10

A receptacle is in the shape of an inverted square pyramid 10 inches in height and with a 6 x 6 square base. The volume of such a pyramid is given by

(1/3) (area of the base) (height)

Suppose that the receptacle is being filled with water at the rate of. 2 cubic inches per second. How fast is water rising when it is 2 inches deep?

+2

Answers (1)

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Triston Dominguez · Answer 1

V = 1/3s^2h; where V is the volume, s is the side length of the square base, and h is the height.

s/h = 6/10 = 3/5

s = 3h/5

V = 1/3 (3h/5) ^2 h = 1/3 (9h^2/25) h = 3h^3/25

dV/dt = 9h^2/25 dh/dt = 0.2 = 1/5

dh/dt = 5 / (9h^2)

When h = 2

dh/dt = 5 / (9 (2) ^2) = 5 / (9 * 4) = 5/36 = 0.1389 inches per seconds.