At points on a circle of radius a, line segments are drawn perpen- dicular to the plane of the circle, the perpendicular at each point P being of length ks, where s is the length of the are of the circle measured counterclockwise from (a, 0) to P and k is a positive constant, as shown here. Find the area of the surface formed by the perpendiculars along the arc beginning at (a, 0) and extending once around the circle.

Question
At points on a circle of radius a, line segments are drawn perpen-
dicular to the plane of the circle, the perpendicular at each point P
being of length ks, where s is the length of the are of the circle
measured counterclockwise from (a, 0) to P and k is a positive
constant, as shown here. Find the area of the surface formed by
the perpendiculars along the arc beginning at (a, 0) and extending
once around the circle.

Image Transcription

At points on a circle of radius a, line segments are drawn perpen- dicular to the plane of the circle, the perpendicular at each point P being of length ks, where s is the length of the are of the circle measured counterclockwise from (a, 0) to P and k is a positive constant, as shown here. Find the area of the surface formed by the perpendiculars along the arc beginning at (a, 0) and extending once around the circle.

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MathCalculus

Applications of Integration