A tank in the shape of a hemisphere with a radius r = 7 ft is full of water to a depth of 3 ft. Set up the integral that would find the work W required to pump the water out of the spout. Use the location of the origin and the direction of the positive axis as specified in the different parts. hemisphere Note: Use 62.5 lb/ft3 as the weight of water.

(A) The origin is at the top of the tank with positive y variables going down. dy
(B) The origin is at the bottom of the tank with positive y-values going up. dy

Abucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 6(t), where t represents time in minutes and p represents how far the paint is spreading. the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = 3.14(p)^2 part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. part b: how large is the area of spilled paint after 8 minutes? you may use 3.14 to approximate pi in this problem.