b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² • Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r (You do not need to enter this answer into WebAssign.) o Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r V = f (x) dx What would a, b and f(x) be? a = -r b = r f(x) = sqrtr^(2)-x^(2) (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3

b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² • Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r (You do not need to enter this answer into WebAssign.) o Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r V = f (x) dx What would a, b and f(x) be? a = -r b = r f(x) = sqrtr^(2)-x^(2) (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 23E

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