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Math 366 Chapter 13 Review Problems

1. Complete the following.

a. 45 ft = _____ yd

b. 947 yd = _____ mi

c. 0.25 mi = _____ ft

d. 289 in. = _____ yd

e. 7 km = _____ m

f. 173 cm = _____ m

g. 67 cm = _____ mm

h. 132 m = _____ km

2. Given three segments of length p, q, and r, where p > q, determine whether it is possible to

construct a triangle with sides of length p, q, and r in each of the following cases. Justify

your answers.

a. p – q > r

b. p – q = r

3. Determine the area of the shaded region on each of the following geoboards if the unit of

measure is 1 cm2.

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4. Explain how the formula for the area of a trapezoid can be found by using the following

figures:

5. Lines a, b, and c are parallel to the line containing side AB of the triangles shown.

List the triangles in order of size of their areas from least to greatest. Explain why your

order is correct.

6. Use the figure shown to find each of the following areas:

a. The area of the regular hexagon

b. The area of the circle

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7. Find the area of each shaded region in the following figures.

8. Find the surface area of the following box (include the bottom):

9. A baseball diamond is actually a square 90 ft on a side. What is the distance a catcher must

throw from home plate to second base?

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10. Find the length of segment AG in the spiral shown.

11. For each of the following, determine whether the measures represent sides of a right

triangle. Explain your answers.

a. 10 in., 24 in., 26 in.

b. 40 cm, 60 cm, 104 cm

12. Find the surface area and volume of each of the following figures:

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13. Find the lateral surface area of the following right circular cone:

14. Doug’s Dog Food Company wants to impress the public with the magnitude of the

company’s growth. Sales of Doug’s Dog Food doubled from 2000 to 2003, so the company

is displaying the following graph, which shows the radius of the base and the height of the

2003 can to be double those of the 2000 dog food can. What does the graph really show

with respect to the company’s growth? Explain your answer.

15. Find the area of the kite shown in the following figure:

16. The diagonal of a rectangle has measure 1.3 m. and a side of the rectangle has measure 120

cm. Find the following:

a. Perimeter of the rectangle

b. Area of the rectangle

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17. Find the area of a triangle that has sides of 3 m, 3 m, and 2 m.

18. A poster is to contain 0.25 m2 of printed matter, with margins of 12 cm at top and bottom

and 6 cm at each side. Find the width of the poster if its height is 74 cm.

19. A right circular cylinder and a right circular cone share a circular base and have the same

volume. What is the height of the cone?

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20. Use a coordinate system to locate triangle ABC with vertices having coordinates A (0, 0 ), B

(8, 0), and C (6, 10).

a. Write equations for each of the sides of the triangle.

b. Find the midpoints of the sides of the triangle.

c. Write the equations of each of the medians of the triangle.

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21. On a 5 × 5 geoboard,

a. Find a polygon whose perimeter is greater than 16.

b. Find a polygon with least perimeter. What is the perimeter?

c. Find the polygon with greatest area.

22. What is the length of the diagonal of a 8 ½ × 11-in. page of typing paper?

23. What is the circumference of the circumcircle of a triangle whose sides have length 6, 8, and

10 in.?

24. What is the radius of a circumcircle for an equilateral triangle of side 6 in.?

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25. Consider a three-dimensional “geospace board.” If it is 5 × 5 × 5, what is the length of the

diagonal?

26. Complete each of the following:

a. A cube whose length, width, and height are each 1 cm has a volume of _______.

b. If the cube in (a) is filled with water, the mass of the water is _______.

c. If a car uses 1 L of gas to go 12 km, the amount of gas needed to go 300 km is _____ L.

d. 47.8 L = _____ cm3

e. 20 km2 = _____ m

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f. 37 L = _____ mL

g. 7140 mL = _____ L

h. 23 m3 = _____ cm

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i. 64 cm3 = _____ mL

j. 48,762 g = _____ kg

k. 3900 kg = _____ g

27. Two cones are defined to be similar if the ratio between their heights equals the ratio

between their radii. If two similar cones have heights h1 and h2, find the ratio between

their volumes in terms of h1 and h2.

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28. a. A tank that is a right rectangular prism is 1 m × 2 m × 3 m. If the tank is filled with

water, what is the mass of the water?

b. Suppose the tank is exactly half full of water and then a heavy metal sphere of radius

30 cm is put into the tank. How high is the water now if the height of the tank is 3 m?

29. Complete each of the following:

a. 3 dm3 of water has a mass of _____ g.

b. 1 L of water has a mass of _____ g.

c. 5 cm3 of water has a mass of _____ g.

d. 7.3 ml of water has a mass of _____ kg.

e. 0.6 L of water has a volume of _____ m3.