Question

A milk carton is shaped like a tall box with a triangular prism on top. The sides of the top section are isosceles triangles. This particular milk carton has a 5 inch × 5 inch square base, and is 11 inches tall. (See the picture.) in 8 in Suppose you're filling the carton with liquid at a rate of 10 inches3 per minute. In this problem, you'll figure out the rate of change of the height of the liquid in the carton, at the instant when the carton holds 220 inches3 of liquid b in o in (a) Let y be the height of the liquid in the carton. Then y is a function of time, because 1. y is changing as more liquid pours in. Suppose y < 8, so that the liquid is all in the rectangular part of the carton. Find a formula for the total volume of liquid in the carton (b) Now suppose 8 < y < 11, so that some liquid is in the triangular part of the carton. Find a formula for the total volume of liquid in the carton, in terms of y. You might want to break up the volume into two pieces: the volume below the 8-inch line and the volume above the 8-inch line.

Answer 1

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