An hourglass is made up of two glass cones connected at their tips. Both cones have...

 

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An hourglass is made up of two glass cones connected at their tips. Both cones have radius I inch and height 3 inches. When the hourglass is flipped over, and starts falling to the lower cone. (a) When the sand remaining in the upper cone has height y inches, its volume A in terms of y is (b) When the sand in the lower cone has reached a height of h inches, its volume 8 in terms of his (Hint: is the volume of the bottom cone minus the volume of the empty space above the sand.) (c) Assume the total volume of sand in the hourglass is 3/4 cubic inches. Also, assume the height of the sand in the upper cone is decreasing at a rate of 9/100 inches per second. At the instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is increasing at a rate of inches per second. An hourglass is made up of two glass cones connected at their tips. Both cones have radius I inch and height 3 inches. When the hourglass is flipped over, and starts falling to the lower cone. (a) When the sand remaining in the upper cone has height y inches, its volume A in terms of y is (b) When the sand in the lower cone has reached a height of h inches, its volume 8 in terms of his (Hint: is the volume of the bottom cone minus the volume of the empty space above the sand.) (c) Assume the total volume of sand in the hourglass is 3/4 cubic inches. Also, assume the height of the sand in the upper cone is decreasing at a rate of 9/100 inches per second. At the instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is increasing at a rate of inches per second.