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Revolved

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AP Calculus AB/BC

Definition

To revolve means to rotate an object around an axis, resulting in the creation of a three-dimensional solid shape.

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Practice Questions (7)

Consider a region defined by the function f(x) = x^3, revolved around the x-axis from x = 1 to x = 2. What is the volume of the solid formed by this revolution?
Consider a region defined by the function f(x) = x^2, revolved around the x-axis from x = 0 to x = 1. What is the volume of the solid formed by this revolution?
Consider a region defined by the functions g(x) = x^3 and h(x) = 2x^3, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
Consider a region defined by the functions f(x) = 2x and h(x) = 3x, revolved around the x-axis from x = 0 to x = 2. What is the volume of the resulting solid?
Consider a region defined by the functions f(x) = x^2 and h(x) = 2x, revolved around the x-axis from x = 0 to x = 3. What is the volume of the resulting solid?
If a region defined by the functions g(y) = √(4-y^2) and k(y) = √(9-y^2) is revolved around the w-axis from y = 0 to y = 2, what is the volume of the resulting solid?
What defines the boundaries of the region being revolved in the Washer Method?

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