zMath 180  - Unit 17: Derive Formulas
In the first three problems, find SURFACE AREA using a formula. It may be helpful to sketch the figure first. Label the answers correctly.

1) What is the SURFACE AREA of the solid with the given measurements?

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2) What is the SURFACE AREA of the solid with the given measurements?

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3) What is the SURFACE AREA of the solid with the given measurements?

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In the next three problems, find the VOLUME using a formula. Use the basic formula for the volume of prisms (“V = Bh”, where “B” represents the area of the base and “h” represents the height) to build a formula for each different solid. It may be helpful to sketch the figure first. Label the answers correctly.

4) What is the VOLUME of the solid with the given measurements?

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5) What is the VOLUME of the solid with the given measurements?

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6) What is the VOLUME of the solid with the given measurements?

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In the next three problems, find SURFACE AREA using a formula. It may be helpful to sketch the figure first. Label the answers correctly.

7) What is the SURFACE AREA of the solid with the given measurements? Round the answer to the nearest whole square centimeter.

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8) What is the SURFACE AREA of the solid with the given measurements? Round the answer to the nearest whole square millimeter.

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9) What is the SURFACE AREA of the solid with the given measurements?

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10) Which of the three previous problems has the most precise measurements given?

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For the next four problems, calculate the VOLUME and be sure to label the answer correctly. Remember that the volume formulas are based on the basic formula, V = Bh, where “B” represents the area of the base and “h” represents the height of the solid.

11) What is the VOLUME of the solid with the given measurements?.

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12) What is the VOLUME of the solid with the given measurements?

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13) What is the VOLUME of the solid with the given measurements?

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14) What is the VOLUME of the solid with the given measurements? Recall that the volume of a pyramid is 1/3 as much as the volume of a prism with the same base area and height.

15) A rectangular room is 8 feet high, 10 feet wide, and 10 feet long. Emily bought some wallpaper for the walls. Disregarding doors, windows, and pattern matching, what is the minimum area of wallpaper she could use to cover all the walls?

Review

16) What is the perimeter of the given shape?

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17) What is the perimeter of the given shape?

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18) What is the measure of one interior angle of a regular octagon?

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19) What is the measure of one exterior angle of a regular hexagon?

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For the next two problems, refer to the chart below to change each metric measure to standard measure.

20) 95 meters (m) = _________ yards (yd)

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21) 4.2 kilometers (km) = _________ miles (mi)

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22) Find the product.

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23) Find the product.

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24) Find the product.

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25) Find the sum.

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26) Find the sum.

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27) Find the sum.

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In the next six problems, line “r” and line “s” are parallel lines cut by transversal “t”.

28) Name four pairs of vertical angles.

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29) Name four pairs of corresponding angles.

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30) Name two pairs of alternate interior angles.

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31) List all angles that are congruent to angle 1.

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32) Name four pairs of supplementary angles.

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33) If the measure of angle 2 is 41 degrees, what is the measure of angle 5?

34) Name the solid shape the net will become when constructed.

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35) Name the solid shape the net will become when constructed.

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36) Name the solid shape the net will become when constructed.

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37) Draw a net for a cylinder on paper. Describe the body of the cylinder.

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38) Draw a net for a triangular pyramid on paper. Describe the sides.

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39) Explain how a net is used to show surface area.

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40) The entire circle represents a total of 2875 CD’s sold. Which is the best approximation of the number of CD’s represented by the shaded sector of the circle?

41) Solve the equation for “n” using inverse operations.

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42) Nicholas has 425 pennies. This is 53 more than 6 times the number of pennies Chloe has. How many pennies does Chloe have? Write an equation to solve the problem, and then solve.

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43) Which graph represents the inequality, p > –2. State the letter of the correct answer.

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44) True or False. The point –1.5 is included in the set of numbers that are represented by the graph of p > –2.

45) Name a fraction or mixed number that would be included in the set of numbers represented by the graph of p > –2.

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