Cylinder of Cookie Dough

Problems from the Gallery Walk

Cylinder of Cookie Dough

You buy a cylinder of chocolate chip cookie dough at Ukrop’s. You want to roll out the dough to make a long, narrow rope. The original height is 12 in. and the original radius is 2 in. If the radius is decreasing at .03 in/min when the radius is 1 in., what is the rate of change of the height at this moment?

Moving Ships

Two ships are steaming away from a point O along routes that make a 120o angle. Ship A moves at 14 knots (nautical miles per hour; a nautical mile is 2000 yards). Ship B moves at 21 knots. How fast are the ships moving apart when OA = 5 and OB = 3 nautical miles? (Use Law of Cosines.)

Moving Race Car

You are videotaping a race from a stand 132 feet from the track, following a car that is moving at 264 ft/sec. About how fast will your camera angle be changing (a) when the car is right in front of you? (b) ½ second later?

Leaky Conical Tank

Water is poured at the rate of 8 ft3/min into a conical tank, 20 ft deep and 10 ft in diameter at the top. If the tank has a leak in the bottom and the water level is rising at the rate of 1 in/min, when the water is 16 ft deep, how fast is the water leaking?

Rope over a Wall

A rope 35 ft long runs over the top of a wall 12 ft high. Each end of the rope is attached to a cement block on the ground. One block is being pulled away from the wall at the rate of 30 ft/min. At the time that the first block is 16 ft from the base of the wall, how fast is the other block being dragged toward the wall?

Rising Missile

A missile rises vertically from a point on the ground 75,000 feet from a radar station. If the missile rises at a rate of 16,500 feet per minute at the instant when it is 38,000 feet high, what is the rate of change, in degrees per minute, of the missile’s angle of elevation from the radar station at this instant?

Shadow on a Wall

A man 6 ft tall is walking toward a building at the rate of 5 ft/sec. If there is a light on the ground 50 ft from the building, how fast is the man’s shadow on the building growing shorter when he is 30 ft from the building?