Question

(c) find the volume of a sphere of redius 'R' using volume integral ?​

Answer 1

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The sphere of radius r can be obtained rotating the half circle graph of the function y = √ r − x2, x ∈ [−r, r]. about the x-axis. The volume V is obtained as follows:

1. V = ∫ r.
2. -r
3. π( √ r2 − x2)2 dx = 2. ∫ r.
4. π(r2 − x2)dx = (4/3)πr3.