A sphere of radius 3 feet contains grain with a depth of 5 feet. The grain inside weighs 5 pounds per cubic foot.
Find the amount of work in foot-pounds required to empty the trough by lifting it to the top of the sphere.
3 answers
4,725 foot-pounds
AAAaannndd the bot gets it wrong yet again!
at a depth of 3-h, the radius of the cross-section is r^2 = 3^2-h^2
so the work per slice of thickness dh is weight * distance
∫[-3,2] 5π(9-h^2)(3-h) dh = 2125π/4 = 1669
at a depth of 3-h, the radius of the cross-section is r^2 = 3^2-h^2
so the work per slice of thickness dh is weight * distance
∫[-3,2] 5π(9-h^2)(3-h) dh = 2125π/4 = 1669
Thank you!
how did you get the integral with [-3,2]?
how did you get the integral with [-3,2]?