A pyramid has height h and a square base with side x. The volume of a pyramid is $$V = \frac{1}{3}x^2h$$ If the height remains fixed and the side of the base is decreasing by 0.004 meter/yr, what rate is the volume decreasing when the height is 180 meters and the side of the square base is 200 meters? The volume is decreasing at a rate of meters$$^3$$/year
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Given: Volume of a pyramid: $$V = \frac{1}{3}x^2h$$ Height h remains fixed, so $$\frac{dh}{dt} = 0$$. Side of the base is decreasing by 0.004 meter/yr, so $$\frac{dx}{dt} = -0.004$$ meter/yr. Current height: $$h = 180$$ meters. Current side of the square base: $$x Show more…
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