Radius

AP Computer Science A

AP Physics 1

AP Physics C: Mechanics

AP Pre-Calculus

AP Calculus AB/BC - 4.5 Solving Related Rates Problems

AP Calculus AB/BC - 8.8 Volumes with Cross Sections: Triangles and Semicircles

AP Calculus AB/BC - 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis

AP Calculus AB/BC - 8.10 Volume with Disc Method: Revolving Around Other Axes

The volume of a sphere is given by V = (4/3)πr^3. If the radius is increasing at a rate of 4 cm/s, what is the rate of change of the volume with respect to time when the radius is 3 cm?

The radius of a circular pool is decreasing at a rate of 0.25 m/min. At what rate is the area of the pool changing when the radius is 4 m?

A marathon runner is jogging around a circular track with a radius of 60 meters at a constant speed of 4 m/s, while her running partner stands still at the starting point. Exactly 10π seconds after she leaves the starting point, what is the rate of change in the distance between the runner and her partner?

A drop of water in space is currently in the shape of a cylinder with radius 1 mm and height 2 mm. A piston pushes the circular faces of the drop closer together, decreasing the height at a rate of 1 mm/s. If the water stays in the shape of a cylinder and its volume does not change, at what rate is the radius of the drop increasing?

The rate of change of the temperature of a cylindrical rod in Kelvin per second, T, is proportional to the radius of the cylinder in inches, r, and the height of the cylinder in inches, h. If the rate of change of the temperature is 60 Kelvin per second for a rod with radius 3 inches and height 2 inches, what is the differential equation that represents this situation?

The rate of change of the surface area of a sphere with respect to time is proportional to the square of the radius. At t = 0, the radius is 2 cm, and the rate of change of the surface area is 16 cm^2/s. If A(t) is the surface area of the sphere, what is the differential equation that represents this situation?