1. Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 58 m. (Round your answer to two decimal places.)

2.Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm²?

3.A cylindrical tank with radius 3 m is being filled with water at a rate of 3 m³/min. How fast is the height of the water increasing?

4.The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm?

5.A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station. (Round your answer to the nearest whole number.)

6.Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing three hours later?