I need some help with some of my homework questions from tutoring, if you can solve any of these and show your working it would be greatly appreciated.
8. A cap of depth 'h' is cut from a sphere of radius 'r' units. Find its volume. Answer: ((pi*h^(2))*(3r-h))/3
15. The portion of the curve y^2=4ax from (a,2a) to (4a,4a) revolves around the tangent at the origin. Prove that the volume bounded by the curved surface so formed and the ends perpendicular to the axis of revolution is (62*pi*a^(3))/5.
19. Find the volume of the solid generated when the region bounded by y=sinx, 0≤x≤pi/2, the x-axis and the line x=pi/2 is rotated about:
a) the y-axis b) the x-axis c) the line x=2 d) the line y=1. Answers: a) - 2pi, b - (pi)^(2)/4, c - pi*(pi-2), d) pi*(2-pi/4)
20. The region bounded by y=e^(-x) and the lines x=1, y=1 is rotated about x=1. Find the volume generated. Answer: pi*(1-2/e)
Thanks a lot
8. A cap of depth 'h' is cut from a sphere of radius 'r' units. Find its volume. Answer: ((pi*h^(2))*(3r-h))/3
15. The portion of the curve y^2=4ax from (a,2a) to (4a,4a) revolves around the tangent at the origin. Prove that the volume bounded by the curved surface so formed and the ends perpendicular to the axis of revolution is (62*pi*a^(3))/5.
19. Find the volume of the solid generated when the region bounded by y=sinx, 0≤x≤pi/2, the x-axis and the line x=pi/2 is rotated about:
a) the y-axis b) the x-axis c) the line x=2 d) the line y=1. Answers: a) - 2pi, b - (pi)^(2)/4, c - pi*(pi-2), d) pi*(2-pi/4)
20. The region bounded by y=e^(-x) and the lines x=1, y=1 is rotated about x=1. Find the volume generated. Answer: pi*(1-2/e)
Thanks a lot
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