22M:003 Basic Geometry - Unit 3 Self-Test

1.   Find the volume of the following right circular cone.

2.   If the volume of a sphere has been doubled, by what ratio has the surface area been increased? Explain.

3.   Determine whether the line segment  is perpendicular to the line segment  where  .

4.   Write the vector  in the form  where  and  and  have the same or opposite direction.

5.   Find x in the following figure.

6.   Consider the figure below.

7.   Suppose that two lines tangent to a circle at P and Q respectively meet at M.
Prove that

8.   If each angle of a regular polygon has 140°, how many sides does the polygon have?

9.   Prove that opposite sides of a parallelogram have the same length.

10. Find the area of the following trapezoid.

11. Find  in the following figure where

12. Find the surface area and volume of a tin can that is 6 inches tall and has a diameter of 4 inches.