Calculus Rate of Change Question:
An inverted pyramid is being filled with water at a rate of 70 cubic centimeter per second. The pyramid, at the top, has the shape of a square with side of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 2 cm.

Question

Calculus Rate of Change Question:
An inverted pyramid is being filled with water at a rate of 70 cubic centimeter per second. The pyramid, at the top, has the shape of a square with side of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 2 cm.

anonymous · Answer

let h be the height. 6/8*h is the width at height h. V(h)=h*(6/8*h)^2 / 3. V(h(t))=h(t)*(6/8*h(t))^2 / 3. We know that V'(h)=70; take a derivative, plug in for V'(h), then solve for h'(t) given that h(t)=2.

anonymous · Answer

*V(t)=h(t)*(6/8*h(t))^2 / 3
*V'(t)=70
*V'(t)