Assignment5

# Assignment5

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MATH1821 Mathematical Methods for Actuarial Science I Assignment 5 Due date: 18 November, 2016 1. The disk x 2 + y 2 a 2 is revolved about the line x = b ( b > a ) to generate a solid shaped like a doughnut and called a torus . Find its volume. ( Hint: a - a a 2 - y 2 dy = πa 2 / 2, since it is the area of a semicircle of radius a .) 2. At points on the curve y = 2 x , line segments of length h = y are drawn perpendicular to the xy -plane. (See accompanying figure.) Find the area of the surface formed by these perpendiculars from (0 , 0) to (3 , 2 3). 3. Find a curve through the point (1

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