In the previous part, you developed the Method of Disks for computing the volume of solids of revolution. We will now find an alternative method, the Method of Shells. We will consider the same function f(x)= 4 - x², in the interval [0, 2], as shown in Figure 1, but now, we will first consider the solid of revolution obtained by revolving f(x) around the y-axis is shown in Figure 3. (a) Say we take two circular cookie cutter, one of radius r₁= 1 and the other with radius r2 = 1+ Ar, and use them to cut out a slice of our solid of revolution. What is the 3-dimensional shape of the slice? What is the surface area of this shape? (b) Find a general formula for the surface area of the slice obtained by cutting the solid with cookie cutters of radii r₁ = x and r₂ = r + Ar. Explain all the terms in your formula.²

In the previous part, you developed the Method of Disks for computing the volume of solids of revolution. We will now find an alternative method, the Method of Shells. We will consider the same function f(x)= 4 - x², in the interval [0, 2], as shown in Figure 1, but now, we will first consider the solid of revolution obtained by revolving f(x) around the y-axis is shown in Figure 3. (a) Say we take two circular cookie cutter, one of radius r₁= 1 and the other with radius r2 = 1+ Ar, and use them to cut out a slice of our solid of revolution. What is the 3-dimensional shape of the slice? What is the surface area of this shape? (b) Find a general formula for the surface area of the slice obtained by cutting the solid with cookie cutters of radii r₁ = x and r₂ = r + Ar. Explain all the terms in your formula.²

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 22E

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