Question 1 (10 points) Oil is kept in a conical tank silling on it's circular base....

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Question 1 (10 points) Oil is kept in a conical tank silling on it's circular base. The circular base has a radius of 10 meters and the tank is 20 meters high. Assume this tank is filled to a height of 15 meters. Let the gravitational constant g = 10 and let the density of the oil be p = 500. (a) (3 points) Find the dimensions and the volume of a horizontal slice y meters from the bottom of the tank. (b) (4 points) Find the work required to pump the slice from part (a) out through a hole at the top of the tank. (Your answer should contain the variable y. (c) (3 points) Set up the integral to find the work required to pump all of the oil in the tank out through the hole at the top of the tank. DO NOT EVALUATE THE INTEGRAL! Question 1 (10 points) Oil is kept in a conical tank silling on it's circular base. The circular base has a radius of 10 meters and the tank is 20 meters high. Assume this tank is filled to a height of 15 meters. Let the gravitational constant g = 10 and let the density of the oil be p = 500. (a) (3 points) Find the dimensions and the volume of a horizontal slice y meters from the bottom of the tank. (b) (4 points) Find the work required to pump the slice from part (a) out through a hole at the top of the tank. (Your answer should contain the variable y. (c) (3 points) Set up the integral to find the work required to pump all of the oil in the tank out through the hole at the top of the tank. DO NOT EVALUATE THE INTEGRAL!