3. The radius of a large sphere is increasing at the rate of 8m/ sec. At what rate is the sphere changing surface area when the radius of the sphere is 12m. Solution:

An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 10 cm. Find the rate at which the water level is rising when the water level is 3 cm. cm/sec h b₁ b2

A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the rate of 2 millimeters per second. At the instant that the radius of the tube is 6 millimeters, the volume is increasing at the rate of 967 cubic millimeters per second. Which of the following statements about the surface area of the tube is true at this instant? (The volume V of a cylinder with radius r and height h is V = Tr2h. The surface area Sof a cylinder, not including the top and bottom of the cylinder, is S = 2πrh.) (A) B C (D The surface area is increasing by 28 square millimeters per second. The surface area is decreasing by 287 square millimeters per second. The surface area is increasing by 32π square millimeters per second. The surface area is decreasing by 32π square millimeters per second.

An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is 11 cm. Find the rate at which the water level is rising when the water level is 2 cm. cm/sec h b₁ b₂