Section 2.5, problem 231 For the following exercises, find the mass of the two-dimensional object that is centered at the origin. &. A plate of radius 10 in. with density function p (x) = l + cos (xx) Section 2.5, problem 235 E. A spring has a natural length of 10 cm. It takes 2 J to stretch the spring to 15 cm. How much work would it take to stretch the spring from 15 cm to 20 cm? A full water tank in the shape of an inverted right circular cone is 8 m across the top and 4 m high. How much work is required to pump all the water over the top of the tank? (The density of water is 1000 kg/m3. Assume g = 9.8 m/sz.) **Set up and evaluate** [PHYSICS AND ENGINEERING] Hydrostatic Force. A vertical semicircular plate is in the wall of a swimming pool. The top of the plate is 4 feet below the water level. The radius of the semicircle is 3 feet. Recall that water has a weight density of 62.5 pounds per cubic foot. water level 4 W Set up but DO NOT EVALUATE or even algebraically simplify an integral that represents the total hydrostatic force on the plate. **Set up but do NOT evaluate* *