I. TRUE or FALSE. Write true if the statement is correct, write false otherwise.

1. The axis and the altitude of any given circular cylinder are sometimes equal in measure.

2. The surface area of a pyramid is equal to the sum of the area of the lateral faces and the base of the pyramid.

3. The slant height of a regular pyramid is sometimes equal to the altitude of the pyramid.

4. Every section of any given cone made by a plane passing through its vertex and containing two points of the base is an isosceles triangle.

5. A right section of a cone is a section perpendicular to its base and cutting all the elements.

6. The total area of a prism is the product of lateral edge and the perimeter of the right section.

7. The altitude of a prism is the parallel distance between the planes of its bases.

8. If every section of the solid parallel to the base is equal in area to that of the base and the bases of a solid are equal in area and lie in parallel planes, the volume of the solid is the product of its base and altitude.

9. The lateral edges of a prism are always perpendicular to its bases.

10. An element of a circular cylinder is always perpendicular to its right section.

II. Provide what is asked

11. The edges of a rectangular solid are in the ratio 3:5:7 and the surface area is 840 sq. ft. Find the length of the three edges.

12. The base of a right prism is a right triangle whose legs have the ratio 7:9. The area of the base is 34sq. m. If the altitude of the prism is 10 m. Find its total area.

13. A channel whose cross section is a semicircle with rise of 6 ft. per 1500 ft., is flowing full. The radius of the channel is 57.9in. The vertical plane which contains the axis is perpendicular to the two vertical planes which contain the ends of the channel. If the end planes are 3140 ft. apart, find the amount of water in the channel.

14. Find the (a) lateral area, (b) total area, and (c) volume of the regular hexagonal pyramid PABCDEF if the apothem of the base is 108in. and the lateral edge is 15ft.

15. The volume of a right circular cone is 144pi cu. ft. If the radius of the base is 3.464101615 ft. find the angle between the base and an element.