A particle starts at the origin and moves along the curve y

Question

Question: 1. Find a curve y = g(x), such that when the region between the curve and the x-axis for 0 ≤ x ≤ π is revolved around the x-axis, it forms a solid with volume given by

₀∫^Π Π(4 - 4cos² x)dx

2. A particle starts at the origin and moves along the curve y = 2x^3/2/3 in the positive x-direction at a speed of 3 cm/sec, where x, y are in cm. Find the position of the particle at t = 6.