zMath 180  - Unit 16: Surface Area and Volume
In the first four problems, sketch the solid and its net, and then find the SURFACE AREA of the shape given. Label each answer correctly. Remember that surface area is measured in square units.

1) Square prism: 4 cm x 4 cm x 8 cm

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2) Rectangular prism: 3 cm x 4 cm x 5 cm

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3) Cylinder: radius 6 cm, height 5 cm (Round the answer to the nearest whole square centimeter.)

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4) Cube: edge 5 cm

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In the next four problems, refer to the sketches of the solids for the previous problems and find the VOLUME of the shapes. Label each answer correctly. Remember that volume is measured in cubic units.

5) Square prism: 4 cm x 4 cm x 8 cm

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6) Rectangular prism: 3 cm x 4 cm x 5 cm

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7) Cylinder: radius 6 cm, height 5 cm (Round the answer to the nearest whole cubic centimeter.)

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8) Cone: radius 6 cm, height 5 cm (Round the answer to the nearest whole cubic centimeter.)

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In the next two problems, the measurement of the edge of the same square is given in different units. Find the area and label each answer correctly. Remember, area is measured in square units.

9) Find the area of a square with a side length of 3 centimeters.

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10) Find the area of a square with a side length of 30 millimeters

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11) Look back to the previous two problems, and then decide which measurement gives a more precise answer for the area of the same shape, 3 centimeters or 30 millimeters?

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12) If the base area of a square prism is 15 square centimeters and the height is eight centimeters, what is the volume of the prism?

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13) If the base area of a square prism is 16 sq cm and the height is 20 centimeters, what is the volume of the prism?

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14) If the base area of a cylinder is 15.6 square centimeters and the height is four centimeters, what is the volume of the cylinder?

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15) If the base area of a cylinder is 1.2 square centimeters and the height is three centimeters, what is the volume of the cylinder?

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16) Matthew owns a tent company and is canvassing an A-Frame tent for a customer. The tent is eight feet high and has a rectangular bottom that measures 12 feet wide by 10 feet. The sides of the tent are 10 feet long. What is the area of the surface that he plans to canvass?

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17) When filled to maximum capacity, a silo can hold about 4,000 cubic meters of corn. The radius of the silo is 8 meters. To the nearest meter, what is the approximate height (h) of the silo?

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Review

For the next three problems, use the given nets to identify the 3-D shape they will become when constructed. Select the letter of the correct net.

18) Square Pyramid

19) Cone

20) Cylinder

On paper, draw a net for a cube, triangular pyramid, and a rectangular prism; and then answer the next three questions.

21) Cube. What shapes are the faces made from?

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22) Triangular pyramid. What shapes are the faces made from?

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23) Rectangular prism. What shapes are the faces made from?

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24) Find the square root.

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25) Find the square root.

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26) Find the square root.

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27) What is 10% of 500?

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28) What is 55% of 80?

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29) What is 20% of 88?

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30) Find the product.

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31) Find the product.

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32) Find the quotient.

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33) Find the quotient.

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

34) True or False. The given angles are congruent.

35) True or False. The given angles are congruent.

36) True or False. The given angles are congruent.

37) What is the area of a circle with a radius of four centimeters?

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38) What is the area of a triangle with a height of four centimeters and a base of three centimeters?

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For cell phone access, Sarah selected the National Freedom Plan that costs $59.99 per month. Use the chart below to answer the next three problems.

39) With a two-year agreement, Sarah can add up to 4 lines for $9.99 each. Her first monthly bill totals 89.96. Sarah did not exceed the “anytime minutes” limit and did not engage in “text messaging”. How many lines did she add to her plan? Write an equation, and then solve.

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40) Sarah's bill for the following month was $124.96 which included additional minutes, but no text messaging. How many additional minutes did she use? Write an equation, and then solve.

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41) Sarah's bill for the month of October included a text messaging charge. With text messaging, the people on Sarah’s plan can send and receive text messages, but charges are made for both outgoing and incoming calls. Sarah’s daughter, Brianna, sent and received text messages from her friends which totaled $2.50. How many text messages did Brianna send and receive? Write an equation, and then solve.

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42) Solve for “n” using inverse operations.

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43) Solve for “m” using inverse operations.

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44) Which inequality represents the solution to 44 > y – 5?

45) Which inequality represents the solution to the given inequality? State the letter of the correct answer.

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