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Height

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AP Calculus AB/BC

Definition

The height of an object or shape refers to its vertical measurement, from the base to the top.

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Practice Questions (3)

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 height h of a tree with respect to time t is directly proportional to the natural logarithm of h. Which of the following differential equations represents this situation, where k is a proportionality constant?
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?

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