1. The volume of an ellipsoid with axes of length 2a, 2b, and 2c is V = πabc. Find the percentage change in the volume when a increases by 2%, b increases by 1.5%, and c decreases by 2.5%. 2. A...

1. The volume of an ellipsoid with axes of length 2a, 2b, and 2c is V = πabc. Find the percentage change in the volume when a increases by 2%, b increases by 1.5%, and c decreases by 2.5%.

2. A hemispherical tank with a radius of 1.50 m is filled with water to a depth of 1.00 m. Water is released from the tank, and the water level drops by 0.05 m (from 1.00 m to 0.95 m).

a. Approximate the change in the volume of water in the tank. The volume of a spherical cap is  where r is the radius of the sphere and h is the thickness of the cap (in this case, the depth of the water).

b. Approximate the change in the surface area of the water in the tank.