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Similar Figures MCQs — Mathematics (page 2)

44 multiple-choice questions on Similar Figures from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. Two similar shapes have corresponding lengths in the ratio 1 : 4. The smaller has area 9 cm². The area of the larger is:

  1. 36 cm²
  2. 576 cm²
  3. 153 cm²
  4. 144 cm²

Answer: D) 144 cm²

Explanation: Area ratio = 1 : 16, so the larger area is 9 16 = 144 cm². SLO M-09-B-17 · Understanding

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27. Two similar triangles: the first has sides 5 cm and 8 cm; the corresponding side to 5 cm in the second is 15 cm. The side corresponding to 8 cm is:

  1. 25 cm
  2. 18 cm
  3. 758 cm
  4. 24 cm

Answer: D) 24 cm

Explanation: Scale factor = 155, so the side is 8 155 = 24 cm. SLO M-09-B-16 · Knowledge

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28. Two similar solids have lengths in the ratio 1 : 5. Their volumes are in the ratio:

  1. 1 : 125
  2. 1 : 25
  3. 1 : 15
  4. 1 : 5

Answer: A) 1 : 125

Explanation: Volumes scale by the cube: 5^3 = 125. SLO M-09-B-16 · Knowledge

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29. Which pair of figures is always similar?

  1. two isosceles triangles
  2. two rectangles
  3. two rhombuses
  4. two squares

Answer: D) two squares

Explanation: All squares have 90^circ angles and equal sides, so one is always an enlargement of another. SLO M-09-B-16 · Knowledge

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30. A photo 10 cm × 15 cm is enlarged so that its width becomes 20 cm. The area of the enlargement is how many times the original?

  1. 8 times
  2. 3 times
  3. 2 times
  4. 4 times

Answer: D) 4 times

Explanation: Scale factor 2, so area factor 2^2 = 4. SLO M-09-B-17 · Understanding

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31. Two similar shapes have corresponding lengths in the ratio 1 : 2. The smaller has area 20 cm². The area of the larger is:

  1. 160 cm²
  2. 40 cm²
  3. 80 cm²
  4. 100 cm²

Answer: C) 80 cm²

Explanation: Area ratio = 1 : 4, so the larger area is 20 4 = 80 cm². SLO M-09-B-17 · Understanding

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32. A map has scale 1 : 10,000. A park on the map has area 6 cm². Its real area is:

  1. 600 m²
  2. 60 000 cm²
  3. 6000 m²
  4. 60 000 m² (6 hectares)

Answer: D) 60 000 m² (6 hectares)

Explanation: Real area = 6 10,000^2 cm² = 600,000,000 cm² = 60,000 m². SLO M-09-B-17 · Understanding

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33. The volumes of two similar cones are in the ratio 8 : 27. Their surface areas are in the ratio:

  1. 8 : 27
  2. 4 : 9
  3. 64 : 729
  4. 2 : 3

Answer: B) 4 : 9

Explanation: Length ratio = [3]8 : [3]27 = 2 : 3; area ratio = 4 : 9. SLO M-09-B-17 · Understanding

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34. If two similar cubes have edges 2 cm and 6 cm, the ratio of their volumes is:

  1. 1 : 9
  2. 1 : 3
  3. 1 : 6
  4. 1 : 27

Answer: D) 1 : 27

Explanation: Length ratio 1 : 3; volume ratio 1 : 27. SLO M-09-B-16 · Knowledge

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35. Two similar shapes have corresponding lengths in the ratio 3 : 5. The smaller has area 18 cm². The area of the larger is:

  1. 50 cm²
  2. 30 cm²
  3. 2503 cm²
  4. 68 cm²

Answer: A) 50 cm²

Explanation: Area ratio = 9 : 25, so the larger area is 18 259 = 50 cm². SLO M-09-B-17 · Understanding

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36. For two similar triangles, which condition is enough?

  1. all three pairs of corresponding angles are equal
  2. one pair of sides is equal
  3. one angle is equal
  4. the perimeters are equal

Answer: A) all three pairs of corresponding angles are equal

Explanation: Equal angles (AA) force the sides to be in proportion for triangles. SLO M-09-B-16 · Knowledge

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37. Two similar jugs have capacities 1 litre and 8 litres. The small jug is 12 cm tall. The large jug is:

  1. 96 cm tall
  2. 48 cm tall
  3. 36 cm tall
  4. 24 cm tall

Answer: D) 24 cm tall

Explanation: Volume ratio 1 : 8 means length ratio 1 : 2, so 12 2 = 24 cm. SLO M-09-B-17 · Understanding

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38. The scale factor that enlarges a 3 cm side to a 12 cm side is:

  1. 9
  2. 36
  3. 14
  4. 4

Answer: D) 4

Explanation: 12 div 3 = 4. SLO M-09-B-16 · Knowledge

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39. Two similar shapes have corresponding lengths in the ratio 4 : 5. The smaller has area 32 cm². The area of the larger is:

  1. 1252 cm²
  2. 50 cm²
  3. 82 cm²
  4. 40 cm²

Answer: B) 50 cm²

Explanation: Area ratio = 16 : 25, so the larger area is 32 2516 = 50 cm². SLO M-09-B-17 · Understanding

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40. Two similar figures have corresponding lengths in the ratio 1 : 3. Their areas are in the ratio:

  1. 1 : 27
  2. 1 : 9
  3. 1 : 6
  4. 1 : 3

Answer: B) 1 : 9

Explanation: Areas scale by the square of the length ratio: 1^2 : 3^2 = 1 : 9. SLO M-09-B-16 · Knowledge

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41. The volumes of two similar cones are in the ratio 1 : 64. Their surface areas are in the ratio:

  1. 1 : 16
  2. 1 : 4096
  3. 1 : 4
  4. 1 : 64

Answer: A) 1 : 16

Explanation: Length ratio = [3]1 : [3]64 = 1 : 4; area ratio = 1 : 16. SLO M-09-B-17 · Understanding

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42. Two similar figures have corresponding lengths in the ratio 1 : 4. Their areas are in the ratio:

  1. 1 : 64
  2. 1 : 8
  3. 1 : 4
  4. 1 : 16

Answer: D) 1 : 16

Explanation: Areas scale by the square of the length ratio: 1^2 : 4^2 = 1 : 16. SLO M-09-B-16 · Knowledge

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43. Are a 3 5 rectangle and a 6 8 rectangle similar?

  1. Yes, because their perimeters differ
  2. Yes, because all rectangles have right angles
  3. It cannot be decided
  4. No, because 63 neq 85

Answer: D) No, because 63 neq 85

Explanation: Rectangles always have equal angles, so they are similar only if the sides are in the same ratio. SLO M-09-B-16 · Knowledge

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44. The areas of two similar triangles are in the ratio 16 : 25. Their corresponding sides are in the ratio:

  1. 4 : 5
  2. 64 : 125
  3. 8 : 12
  4. 16 : 25

Answer: A) 4 : 5

Explanation: Length ratio = 16 : 25 = 4 : 5. SLO M-09-B-17 · Understanding

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