MATH Integrated Math I  - Unit 23: Surface Area
Some of the questions in this unit may be answered by recording an audio file. If you chose to record the answer, click on the Add Recording button and follow the on-screen instructions closely. Once you have completed and attached the recording, enter the word “COMPLETE” in the text box. (Note: If your computer does not have a built-in microphone, a microphone or microphone/headset combination is needed to record audio.)

For all problems that have formulas that include “pi”, use 3.14. Also, label all answers appropriately.

Surface Area and Nets

1) The shaded figure is a net that can be used to form a rectangular prism. What is the surface area of the prism?

2) The given figure is a net that can be used to form a cylinder. What is the surface area of the cylinder?

3) The given figure is a net that can be used to form a pyramid. What is the surface area of the pyramid?

4) The given figure is a net that can be used to form a cone. What is the surface area of the cone? Express the answer rounded to the nearest tenth.

Surface Area of Prisms and Cylinders

5) Name the solid, and then find the surface area.

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6) Name the solid, and then find the surface area.

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7) Name the solid, and then find the surface area.

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8) What is the surface area of a cylinder with a diameter of 16 centimeters and a height of 1.5 centimeters? Express the answer rounded to the nearest tenth.  (Note: A diameter is given, so adjust the measurement to a radius, and then apply the surface area formula.)

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9) What is the surface area of a cube with an edge length of 8 inches?  (Note:  Since all faces have the same area, the formula for surface area of a cube may be used:  SA = 6e^2 where e^2 means e-squared.)

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10) If the length of the edge of a cube is 11 centimeters, what is the surface area?

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11) All of the dimensions of Prism B are double the dimensions of Prism A. Since all of the dimensions are doubled, would the surface area be doubled as well? Calculate the surface area of both prisms, and then divide to see how many times larger the surface area of the larger prism is than the smaller one.  Use the calculations to provide an explanation to support an answer of yes or no.

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12) How much paper is needed to cover the LATERAL surface of a can of tomato juice if the can is 7 inches tall and has a diameter of 4 inches? Express the answer rounded to the nearest tenth.

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13) Melissa's birthday present to her sister was a new printer for her computer. The printer was in a rectangular box: 1.6 feet x 1 foot x 1.5 feet. How much paper was needed to wrap the gift?

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14) Jerry owns a tent company. He is canvassing an A-frame tent for a customer. The tent is 4 feet high and has a rectangular bottom of 8 feet wide by 7 feet long. The sides of the tent are 8.5 feet long. How much canvas does he need to make the tent?

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15) What is the missing dimension for the given triangular prism that has a surface area of 284 square inches?.

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16) What is the missing dimension for the given cylinder that has a surface area of 485 square centimeters? Express the answer rounded to the nearest tenth.

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17) The solid shown below is composed of a rectangular prism and a triangular prism. What is the surface area of the solid EXCLUDING the bottom face of the solid and any faces of the prisms that are inside the solid? (Hint:  The faces that must be considered are the four walls of the house and the four faces of the roof.)

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Surface Area of Pyramids and Cones

18) What is the surface area of the square pyramid?

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19) Pyramids in Egypt were built thousands of years ago as burial tombs for the pharaohs. The Great Pyramid, the largest pyramid in the world, was built for a pharaoh named Khufu. It has a square base that measures 754 feet on each side and a slant height of 611 feet. What is the total surface area of the Great Pyramid?

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20)

What is the surface area of the cone?  Express the answer rounded to the nearest tenth.

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21) What is the surface area of the cone that has a radius of 16 centimeters and a slant height of 35.1 centimeters?  Express the answer rounded to the nearest tenth.

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22) The students at Barnesville High are making a megaphone for the football game. The megaphone's shape is a cone closed at the vertex with an open base. They are decorating the cone with colorful construction paper. How much paper will they need just to cover the megaphone?

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23) Yummy's ice cream shop sells sugar cones. The cones have a slant height of 6 inches and a radius of 1.5 inches. The owner is going to buy special napkins that will fit around the cone TWO times. The net for the napkin is drawn below. What is the area of the napkin?

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24) What is the slant height of a regular pyramid that has a surface area of 684 square meters and a square base with an edge of 18 meters?

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25) The given solid is an octahedron It is composed of two regular pyramids with a square base measuring 36 feet on one edge. The slant height of the two pyramids is 45 feet. What is the total surface area? (Note: The bases are not included in the surface area since they are inside the solid.)

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26) The given solid is composed of a cylinder as well as a cone. What is the total surface area?  (Note:  Do not include any faces inside the solid.) Express the answer rounded to the nearest tenth.  

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Surface Area of Spheres

27) What is the surface area of a sphere with a radius of 1.5 inches? Express the answer rounded to the nearest tenth.

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28) The Earth's equator can be considered the great circle that divides the earth into two hemispheres, the northern hemisphere and the southern hemisphere. The diameter of the earth at the equator is 12,756.3 kilometer. What is the surface area of the earth? Express the answer rounded to the nearest tenth.

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29) The surface area for the given sphere is 500 square centimeters. What is the radius? Express the answer rounded to the nearest tenth.  

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30) The given sphere with a radius of 6 meters is divided into two hemispheres. The edge is a great circle. What is the surface area of one of the hemispheres? Express the answer rounded to the nearest tenth.

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Drawing Three-Dimensional Figures

31) The drawing represents a box in the shape of a rectangular prism that has been unfolded and lain flat. The blue areas represent the bottom and the lid of the box. The brown areas represent the sides of the box. Each square is one unit in length. What are the length, width, and height of the box?

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The next two activities involve isometric dot paper.  This activity can be completed by using the isometric dot paper online tool located at the Illuminations website.  illuminations.nctm.org Also, a link to print out isometric dot paper is provided in the content area.

Once the activity is completed, take a screen shot of your work by pressing the PrtScr (Print Screen) button on your keyboard.  Then, in your word-processing software, open a blank page, and then select the menu option, Edit/Paste. The screenshot will appear in your document and then you can save it.  Upload that file for the appropriate problem so that your instructor can view your work.

32) Using the online isometric dot paper tool, draw a cube that measures three units on each edge.  Attach a screenshot of the results. The figure is started in the picture below.

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33) Use the three views of the solid shown below to draw the 3-dimensional view of the solid using the online isometric dot paper tool. Each square is one unit long. (a) If you were building this object with one-unit cubes, how many cubes are needed to build the object? (b) Attach a screenshot of the figure you created. (Note:  Part of the side of the figure has been constructed in the figure below.)

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