Questions

1) Which three-dimensional model can be constructed from the two-dimensional views shown below? State the letter of the correct answer.

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2) Which three-dimensional model can be constructed from the two-dimensional views shown below? State the letter of the correct answer.

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3) Which two-dimensional view could be used to construct the three-dimensional model shown below? State the letter of the correct answer.

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4) Which two dimensional view can be used to construct the three dimensional corner view model shown below? State the letter of the correct answer.

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5) Use the three views of the solid shown below and sketch the 3-D figure on isometric dot paper. Each square is one unit long. Describe your drawing by stating the total number of cubes in the figure and how the cubes are arranged by layers.

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6) Which figure is NOT a polyhedron? State the letter of the correct answer.

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7) Answer the following questions about the pentagonal prisms shown below: (a) The arrow is pointing to a base in which prism? (b) The arrow is pointing to a lateral face in which prism? (c) The arrow is pointing to a lateral edge in which prism?

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8) Identify each three-dimensional shape described below. State the number of each figure, and then the name of the shape described.

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9) If a plane slices a regular pyramid as shown below and forms a quadrilateral such that sides “q” and “r” are parallel, what kind of quadrilateral is formed where the plane intersects the pyramid?

a.) square

b.) trapezoid

c.) parallelogram

d.) rhombus

10) What shape is formed by the cross-section of the cube?

a.) square

b.) trapezoid

c.) parallelogram

d.) rhombus

11) If a plane passes through a cube such that it intersects three of the edges of the cube and splits the cube into two parts, what solid is formed with the piece of the cube that contains one vertex?

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12) All the faces in a regular polyhedron (are or are not) congruent?

a.) are

b.) are not

13) Identify each platonic solid described below. State the number of each solid and the name of the solid that is described.

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14) Research the Internet to find the answer to the following questions: The Platonic solids are sometimes also called "cosmic figures". Plato, the Greek mathematician for whom the Platonic Solids are named, equated the cube to the “earth”. To what did he equate (a) the tetrahedron, (b) the icosahedron, (c) the octahedron, and (d) the dodecahedron?

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15) Print out the net below. Cut it out and fold along the edges. Use the flaps to tape the edges together to form a platonic solid. What platonic solid is constructed?

a.) tetrahedron

b.) hexahedron

c.) octahedron

d.) dodecahedron

e.) icosahedron

16) The figure shown below is the net of a rectangular prism. What is the surface area of the prism?

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17) The figure shown below is the net of a right triangular prism. What is the surface area of the prism?

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18) The figure shown below is the net of a right cylinder. What is the surface area of the cylinder? (Recall: The length of the rectangle equals the circumference of the circular base.)

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19) Which solid matches the net shown below? State the letter of the correct answer.

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20) A standard die is used in various board games. The opposite faces are numbered so that the sum is 7. Which figure represents the net for a standard die? State the letter of the correct answer.

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21) Which of the following statements is true?

a.) Surface area is the total area of the lateral faces of a prism.

b.) Lateral area is the total area of the bases of a prism.

c.) Surface area is the total area of the lateral faces and the bases of a prism.

d.) Lateral area is the total area of the lateral faces and the bases of a prism.

22) What is the lateral area of the right hexagonal prism shown below?

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23) What is the surface area of the right triangular prism shown below?

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24) How much heavy plastic is needed to cover the top, the sides, the front, and the back of a green house with the dimensions given below? Round the answer to the nearest tenth. (Hint: Use the Pythagorean Theorem to find the height of the triangular area of the front and the back of the greenhouse.)

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25) In a roll of aluminum foil, the inner cardboard tube has a diameter of 1.75 inches and a height of 18 inches. If the tube is cut and unfolded to form a rectangle, what is the lateral area?

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26) What is the surface area of a cylinder with a diameter of 22 centimeters and a height of 2.5 centimeters?

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27) The surface area of the can shown below is 209 square inches. If the height of the can is 8 inches, what is the radius? Round the answer to the nearest hundredth. (Hint: You will need to use the quadratic formula to solve.)

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28) A company has 20,000 square feet of aluminum to use for making “soda” cans. Each can has a diameter of 2.5 inches and a height of 4.75 inches. How many cans can be made with the aluminum? Assume there is no waste. (Note: 1 square foot = 144 square inches)

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29) Allen wants to create a paper model of a cylinder. He draws two circles, each having a radius of 3 inches. He wants the height of his cylinder to be 6 inches. He must cut out one more part to complete the model. What shape must he cut out of paper and what are the measurements of the shape’s dimensions?

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30) Which is longer, the height of a right pyramid or its slant height? Please explain.

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31) Refer to the regular square pyramid shown below to answer the following questions: (a) What is the length of the slant height of the pyramid? (b) What is the lateral area of the pyramid? (c) What is the surface area of the pyramid? Round the answers to the nearest tenth, when appropriate, and label all answers correctly.

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32) Refer to the regular octagonal pyramid shown below to answer the following questions: (a) What is the lateral area of the pyramid? (b) What is the length of the apothem of the base? (c) What is the area of the base? (d) What is the surface area of the pyramid? Round the answers to the nearest tenth, when appropriate, and label all answers correctly.

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33) Refer to the regular hexagonal pyramid shown below to answer the following questions: (a) What is the length of the apothem of the base? (b) What is the length of one side of the base? (c) What is the area of the base? (d) What is the lateral area? (e) What is the surface area? Round the answers to the nearest tenth, when appropriate, and label all answers correctly.

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34) The polyhedron shown below is one solid formed by joining two congruent regular hexagonal pyramids at their bases. The slant height of both pyramids measures 9 1/2 inches and the length of one edge of the hexagonal base measures 6 3/4 inches. What is the surface area of the polyhedron? (Note: The base area is not included in the surface area because the bases fall within the interior of the polyhedron.)

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35) Explain why the cone shown below is called an “oblique” cone.

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36) Which of the following is the most accurate drawing of the net of a cone?

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37) For the right cone shown below, (a) what is the lateral area and (b) what is the surface area? Round the answers to the nearest tenth and label the answers correctly.

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38) For the right cone shown below, (a) what is the lateral area and (b) what is the surface area? Round the answers to the nearest tenth and label the answers correctly.

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39) Refer to the right cone shown below to answer the following questions: (a) What is the slant height of the cone? (b) What is the lateral area of the cone? (c) What is the surface area of the cone? Round the answers to the nearest tenth and label the answers correctly.

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40) If the surface area of a cone is 2000 sq ft and its slant height is 20 ft, what is the radius of the cone? Round the answer to the nearest tenth and label the answer correctly.

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41) How much material is needed to make a party favor cone that is 3 inches in diameter and has a slant height of 5 inches? Round the answer to the nearest whole inch and label the answer correctly. (Note: The base of the cone is not included.)

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42) Four parts of a sphere are labeled below. State the letter of each part, and then the correct label. Choose from the following terms: great circle, chord, tangent, and diameter.

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43) Refer to the picture of the Earth shown below to answer the following questions: (a) What is the surface area of the Earth to the nearest square mile? (b) Approximately 30% of the Earth’s surface is land. How many square miles of the Earth is land?

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44) Find the minimum amount of material that is used to make a basketball that has a diameter of 9.5 inches. Round the answer to the nearest tenth and label the answer correctly.

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45) A sphere has a great circle with a circumference of 330 centimeters. (a) What is the radius of the sphere? (b) What is the surface area of the sphere? Round the answers to the nearest tenth and label the answers correctly.

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46) If the surface area of a sphere is 978 square feet, what is the length of its radius? Round the answer to the nearest tenth and label the answer correctly.

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47) Sphere A has a radius of 3 and a surface area of 9 “pi”. If the radius of Sphere A is doubled to make Sphere B, the surface area of Sphere B is how many times greater than the surface area of Sphere A?

a.) 3 times greater

b.) 4 times greater

c.) 6 times greater

d.) 8 times greater

48) The rocketry parachute shown below is a hemisphere that is two yards in diameter. Excluding the overlapping of the seams, how much material is used to make the parachute? Round the answer to the nearest tenth and label the answer correctly.

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