Determine the volume of the solid obtained by rotating the portion of the region bounded.

Question

1)  Determine the volume of the solid obtained by rotating the portion of the region bounded by y= \root(3)(x) and y=x/4 lies in the first quadrant about the y-axis

Answer 1

See the video.

Answer 2

√3x = x/4; 3x = x²/16; x = 0 or x = 48.

Volume v = 2π∫₀⁴⁸x(√3x - x/4)dx = 2π(2/5x^5/2·√3 - x³/12)₀⁴⁸ = 3686.4π