Exam 3 Review Sheet
1. Be sure to know the formulas for volume of a prism/cylinder and a pyramid/cone, the
definitions in section 13.1, the Pythagorean Theorem, and the area formulas from previous
chapters.
2. You have 120 feet of fencing to build a pen for your pet. If the fencing you have consists of
straight pieces of wood that can only be connected at right angles, what is the largest area
of the pen that you can construct? If the fencing is flexible and can be bent into curved
pieces, what is the largest area that can be made?
3. Find the number of faces, edges, and vertices of a right trapezoidal prism, and state how
many faces there are of each type of polygon.
4. Find the number of faces, edges, and vertices of a pentagonal bipyramid (two pentagonal
pyramids attached at the base, as in the octahedron being the square bipyramid). Also state
how many faces there are of each type of polygon.
5. Explain why there is no Platonic solid that whose faces are all triangles with six triangles
meeting at each vertex.
6. Draw three distinct two-dimensional patterns that fold and have sides join together to form
a cube.
7. Determine the surface area of a tetrahedron with every edge measuring 1 centimeter.
8. Find the volume of the the following oblique rectangular prism in which the right side of the
top base is directly above the left side of the bottom base.
9. You have a tank of water that is half full before adding toy car to the tank. After adding the
5
toy car, the tank is full. If the tank holds 2 liters of water, how many cm3 is the volume
8
of the toy car?
10. Draw the resulting shape from the following transformations: (a) a translation by the given
vector v, (b) a reflection about the x-axis, and (c) a clockwise rotation about the origin by
90 degrees.
11. Determine the types of symmetry that the following shapes have. Include how many lines
of reflectional symmetry and for what n value for which the shape has n-fold symmetry.
(a) A rectangle that is not a square.
(b) A parallelogram that is not a rectangle or rhombus.
(c) A regular octagon.
12. Draw the lines of symmetry for the following regular pentagon.
13. Explain why the Angle-Side-Angle Criterion causes all triangles with 2 specified angles along
with a specific side length for the side between the 2 angles to be congruent.
14. Draw two examples of triangles showing why triangles with two side lengths being 1 inch and
3 inches as well as having one angle measuring 90◦ are not necessarily congruent. Explain
clearly why your two triangles are not congruent.
15. A model car has a width of 3 inches and a length of 8 inches. If the length of the actual car
is 6 feet, what is its width?