Question: Can you assist with the steps in this problem The equation of the circle of radius r, centered at the origin is x2+y2 = r2.

Can you assist with the steps in this problem

The equation of the circle of radius r, centered at the origin is x2+y2 = r2. (x squared + y squared = r squared.

(a) Sketch the region R in the upper half-plane bounded by the semicircle y = r2 x2 (sqrt r squared - x squared) and the x-axis

(b) Revolve the region R about the x-axis to obtain a sphere of radius r, centered at the origin.

(c) show, using integration techniques, that the volume of the sphere generated is 4/3 r3. (4/3 pi r cubed)

(Hint: Use the fact that the function y = r2 x2 is an even function of x to simplify the integral).

Tutor, kindly give explanation at each step of the process and write legibly.

Thank you

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