Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(7x), y = 4, y = 6, x = 0; about the y-axis v =

Using the disk method, the volume is given by the integral

See the attached image. It shows one such disk generated by the desired revolution. Its volume is , where its radius is (the horizontal distance from the axis of revolution to the curve ) and its height is an infinitesimally small change in , included in the integral as the differential .

We get

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.