A watermelon is in the shape of the ellipsoid whose equation is given by 6x2 + 3y2 + 2z2 = 6. If it is shared equally among 8 members in a family, using integrals, find the volume of each piece of the watermelon.

A farmer is fencing a rectangular area for cattle and uses a straight portion of a river as one side of the rectangle, as illustrated in the figure. Note that there is no fence along the river. If the farmer has 1600 feet of fence, find the dimensions for the rectangular area that gives the maximum area for the cattle. River

Isla wants to build a playhouse that is in the shape of a rectangular pyramid that has the maximum volume possible. The perimeter of the base must be 24 feet. The height of the playhouse should be 2 times the length. What should the dimensions of the play house be? a. 3 feet wide by 9 feet long by 18 feet high b. 6 feet wide by 6 feet long by 12 feet high c. 5 feet wide by 7 feet long by 14 feet high d. 4 feet wide by 8 feet long by 16 feet high