November 2016

A reservoir is in the form of frustum of a cone, 68 ft. across the top, 35 ft. across the bottom, and 18 ft. deep. Find the cost of lining it with tile at $1 per square foot.

From a cylindrical jar 4 in. high and 6 in. in diameter, water is poured by tilting the jar until the center of the bottom is at the surface of the water. A plane is passed through the water parallel to both the axis of the jar and the wetted diameter. What the section made by this plane with the water? If the plane has been passed perpendicular to the wetted diameter, what would be the section?

The silo shown in a sketch is an air- and water-tight tower. It consist of a lower cylinder surmounted by a frustum of a cone whose lower base is a upper base of the cylinder. The frustum in turn is surmounted by a cupola consisting of a smaller cylinder whose lower base is the upper base of the frustum. This smaller cylinder is topped by a conical roof. The inside radii of the smaller and larger cylinders are 6 ft. and 12 ft., respectively. The altitudes of the frustum and larger cylinder are 6 ft. and 21 ft., respectively.

Imagine a cube to measure 5 units on an edge, and to have its total surface area blue. Without the aid of a figure or a cubical object answer the following questions.
(A) how many times must you cut completely through the cube to make cubes with measure 1 unit on an edge?
(B) How many of the cubes of question (A) will have:
(a) Three blue faces?
(b) Two blue faces?
(c) One blue face?
(d) No blue faces?