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Nets, surface area and volume

Ten questions of mixed difficulty, covering Surface area and volume. Print it, or work through it on screen — the answer key starts on its own page.

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Nets, surface area and volume

Math 8 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. What faces does the net of a triangular prism have?

    1. a) 3 triangles and 2 rectangles
    2. b) 1 triangle and 3 rectangles
    3. c) 2 triangles and 3 rectangles
    4. d) 2 triangles and 2 rectangles

  2. A triangular prism is 10 cm long. Its ends are right triangles with sides of 3 cm, 4 cm and 5 cm. What is its surface area?

    1. a) 144 cm²
    2. b) 126 cm²
    3. c) 60 cm²
    4. d) 132 cm²

  3. A label covers the curved side of a can, but not its top or bottom. The can has a diameter of 8 cm and a height of 11 cm. Using π ≈ 3.14, what is the area of the label?

    1. a) 376.8 cm²
    2. b) 88 cm²
    3. c) 276.32 cm²
    4. d) 552.64 cm²

  4. A triangular prism is 10 cm long, and each triangular end has sides of 3 cm, 4 cm and 5 cm. What are the three rectangles in its net?

    1. a) three rectangles that are each 5 cm × 10 cm
    2. b) 3 cm × 10 cm, 4 cm × 10 cm and 5 cm × 10 cm
    3. c) three rectangles that are each 4 cm × 10 cm
    4. d) 3 cm × 4 cm, 4 cm × 5 cm and 3 cm × 5 cm

  5. In the net of a cylinder, a rectangle wraps around the edges of the two circles. The side of the rectangle that wraps around must be as long as

    1. a) the radius of a circle
    2. b) the circumference of a circle
    3. c) the height of the whole cylinder
    4. d) the diameter of a circle

  6. A cylinder has a diameter of 10 cm and a height of 10 cm. Using π ≈ 3.14, what is its volume?

    1. a) 157 cm³
    2. b) 3140 cm³
    3. c) 314 cm³
    4. d) 785 cm³

  7. What is the surface area of a cube with edges of 4 cm?

    1. a) 48 cm²
    2. b) 64 cm²
    3. c) 96 cm²
    4. d) 16 cm²

  8. A rectangular prism measures 5 cm by 3 cm by 2 cm. What is its surface area?

    1. a) 90 cm²
    2. b) 30 cm²
    3. c) 31 cm²
    4. d) 62 cm²

  9. A tent is shaped like a triangular prism. Each triangular end has a base of 2 m and a height of 1.5 m, and the tent is 3 m long. What is its volume?

    1. a) 4.5 m³
    2. b) 9 m³
    3. c) 6.5 m³
    4. d) 1.5 m³

  10. Which set of six squares folds up into a cube?

    1. a) a row of 4 squares, with 1 square above the first and 1 above the fourth
    2. b) a row of 4 squares, with 1 square above the second and 1 below the third
    3. c) 2 rows of 3 squares, joined along their long edges
    4. d) a row of 6 squares

Answer key · Nets, surface area and volume

Math 8 · maddyhelps.com

  1. c) 2 triangles and 3 rectangles — A triangular prism has a triangle at each end, and each of the triangle's 3 sides is joined to the other end by a rectangle: 5 faces in all. A triangle has 3 sides, so it needs 3 rectangles, not 2, and a prism always has two matching ends.
  2. d) 132 cm² — Each triangular end is ½ × 3 × 4 = 6 cm² — the two shorter sides are the base and the height, because they meet at the right angle. The three rectangles are 3 × 10, 4 × 10 and 5 × 10, which add to 120 cm², so the total is 6 + 6 + 120 = 132 cm². 144 cm² forgets to halve for the triangles, and 126 cm² counts only one end.
  3. c) 276.32 cm² — Unrolled, the label is a rectangle: one side is the height, 11 cm, and the other wraps once around the can, 3.14 × 8 = 25.12 cm. Its area is 25.12 × 11 = 276.32 cm². 552.64 cm² uses 2 × 3.14 × 8, which doubles the diameter as if it were the radius, and 376.8 cm² adds the top and bottom, which the label does not cover.
  4. b) 3 cm × 10 cm, 4 cm × 10 cm and 5 cm × 10 cm — Each rectangle joins one side of the triangle to the matching side of the other end, so it is as wide as that side and as long as the prism: 3 × 10, 4 × 10 and 5 × 10. The rectangles are all the same size only when the triangle's sides are, and pairing the triangle's own sides, 3 × 4 and so on, leaves out the length of the prism.
  5. b) the circumference of a circle — The rectangle curls once around each circle's edge, so the side that wraps must match the whole distance around it: the circumference, π × d. If it were only as long as the diameter, it would cover about a third of the way round. The other side of the rectangle is the height.
  6. d) 785 cm³ — The base is a circle of radius 5 cm, half the diameter, with area 3.14 × 5 × 5 = 78.5 cm², and the volume is 78.5 × 10 = 785 cm³. 3140 cm³ uses the diameter as the radius, which makes the base four times too big, and 314 cm³ multiplies the circumference by the height, which is the area of the curved side, not a volume.
  7. c) 96 cm² — A cube has 6 square faces, each 4 × 4 = 16 cm², so its surface area is 6 × 16 = 96 cm². 64 is 4 × 4 × 4, the volume in cm³ — a different measurement — and 48 cm² counts only the three faces you can see at once.
  8. d) 62 cm² — The prism has three pairs of matching faces: 5 × 3 = 15, 5 × 2 = 10 and 3 × 2 = 6 cm². Two of each is 2 × (15 + 10 + 6) = 62 cm². 31 cm² counts each pair once, which is only half the faces, and 30 is the volume, 5 × 3 × 2, in cm³.
  9. a) 4.5 m³ — The triangular end is the base of the prism, with area ½ × 2 × 1.5 = 1.5 m², and the volume is that times the length: 1.5 × 3 = 4.5 m³. 9 m³ forgets that a triangle is half of a rectangle, and 1.5 m³ stops at the area of the end, which is in square metres, not cubic.
  10. b) a row of 4 squares, with 1 square above the second and 1 below the third — Folding the row of 4 makes the four sides of the cube in a loop, and the two extra squares become the top and the bottom — so one must be above the row and one below it. With both above the row, both fold onto the top and overlap, leaving the bottom open. A row of 6 wraps round past where it started, and a 2 by 3 block has squares that fold on top of each other.