An open tank has the shape of a right circular cone (see figure). The tank is 8 feet across the top and 6 feet high. Water is pumped in through the bottom of the tank. (The water weighs 62.4 lb per cubic foot.) Ay (a) How much work is done to fill the tank to a depth of 1 feet? ft-lb (b) How much work is done to fill the tank from a depth of 5 feet to a depth of 6 feet? ft-lb
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
It is given that weight of the water is,
It is known that,
and
But before that we have to find a relationship between x and y coordinates.
Take 3 coordinates on the cone. Let (x, y) be any point on the line which passes through (0, 0) and (4,6) also.
Note: Width is taken from x=-4 to x=4(i.e. total 8) at y=6.
Therefore,
Therefore volume of element is,
Therefore force element will be,
Let level of water be at y, then water have to move for a distance 6-y.
Therefore, total work done to fill the tank to a depth of 1 feet is,
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
