Calculus Need Help Pls!

Question

Which of the following integrals correctly computes the volume formed when the region bounded by the curves x² + y² = 25, x = 4, and y = 0 is rotated around the y-axis? (4 points)

Answer Choices:

Answer 1

We are given the equation of the circle. From here let us find an equation of x in terms of y, that is,

x = sqrt(25-y^2). When y= 0, x = 5 so when x = 4 this gives us that y =3. We have found our lower and upper bounds of our integral. To find pi(R^2-r^2) draw radius towards axis of rotation to help you see what R and r. From this one will get that R = sqrt(25-y^2) and r = 4. Plug in everything into integral and we are done