Sphere
The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. What is the rate of change of the volume of the cylinder, when the radius is 2 cm and the height is 3 cm?
2π/5
A small spherical meteorite enters the atmosphere. The volume of this meteorite decreases at a rate of 2 cm³/min. How fast is the Surface Area decreasing at this time when the diameter of the meteorite is 10 cm? Hint: (SA of sphere= 4πr²)
-4/5
A right cylindrical tank is filled with water. The tank stands up and has a radius of 20 cm. At what rate does the height of the water in the tank drop when the water is being released at 25 cubic centimeters per second?
-1/16π
A ladder is 20 feet in length and leans against the side of a building. If the bottom of the ladder slides away from the building horizontally at a rate of 4 feet per second, at what rate is the ladder sliding down the building when the top of the ladder is 8 feet from the ground?
___ -√336/2
Water runs into a conical tank at the rate of 9 cubic feet per minute. The tank stands pointed downward and has a height of 10 feet and a base radius of 5 feet. How fast is the water level rising when the water is 6 feet deep?
1/π
Some kids are trying to increase the size of a 6-inch deep tube with a machine that increases the tube's radius 1/1000th of an inch every three minutes. How rapidly is the tube's volume increasing when the diameter is 3.8 inches?
0.024 in³/min
The radius of a right circular cylinder increases at a rate of 0.1 cm/sec, and the height decreases at a rate of 0.2 cm/sec. What is the rate of change of the volume of the cylinder, when the radius is 2 cm and the volume is 12π cubic cm/sec?
0.4π
Two people are walking on two different straight roads that meet at a right angle. Student A approaches that intersection at 2 m/sec and Student B is walking away from the intersection at 1 m/sec. At what rate is the angle, at B, changing when student A is 10 meters from the intersection and student B is 20 meters from the intersection. Transfer your answer into radians per second
18/π