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</center><p>Solution: The graph of the curve is the upper semi-circle of radiuscentered at the origin. Let’s start with some simple surfaces. J. Gonzalez-Zugasti, University of MassachusettsLowell In Section we determined a method for calculating the area of a surface of revolution (Fig). For objects such as cubes or bricks, the surface area of the object is the sum of the areas of all of its faces Section Area of a surface of revolution. Let be a smooth, interval, nonnegative function on an. Lets start with some simple surfacesNow we consider the surface which is obtained by rotating the curve y about the x-axis, f x >for all x in a; b and f′ x is continuous ExampleFind the surface area generated by revolving the curve. A surface of revolution is formed when a curve is rotated about a line. Sometimes both methods can be used and in that case they both give the same result 𝑦=−𝑥2,≤𝑥≤about the 𝑥-axis. Suppose a curve y = f(x) for a x b is revolved about the x-axis. Such a surface is the lateral boundary of a solid of revolution of the type discussed in Sections and Tags Example Find the surface area of the solid obtained by revolving the curve 4y=x2,0≤y≤2 about the y-axis Areas of Surfaces of Revolution. Problem: Find the area of the surface generated by revolving the curve = about the The surface area formula for revolution for x = g (y) on [c, d] about the y-axis is EXAMPLEFind the area of the surface generated by revolving on the interval [3/4,/4] about  Surfaces of Revolution. The lateral surface area of a circular cylinder with The concepts we used to find the arc length of a curve can be extended to find the surface area of a surface of revolution. Surface area is the total area of the outer layer of an object. A surface of revolution is formed when a curve is rotated about a line. Here we will build a way to calculate the area of a surface of the form z = f(x,y) over a region R (Fig). The curve sweeps out a surface indimensions. If the surface area is, we can imagine that painting the surface would require the same amount of paint as does a ﬂat region with area. To find the area of such a surface, I’ll We want to deﬁne the area of a surface of revolution in such a way that it corresponds to our intuition. ≤ ≤.</p></translate>
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