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Similar Figures MCQs — Mathematics

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.

1. Two similar bottles have heights in the ratio 1 : 2. The smaller holds 40 ml. The larger holds:

  1. 360 ml
  2. 160 ml
  3. 80 ml
  4. 320 ml

Answer: D) 320 ml

Explanation: Volume ratio = 1 : 8, so the larger holds 40 8 = 320 ml. SLO M-09-B-17 · Understanding

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2. Two similar triangles: the first has sides 3 cm and 7 cm; the corresponding side to 3 cm in the second is 12 cm. The side corresponding to 7 cm is:

  1. 16 cm
  2. 28 cm
  3. 367 cm
  4. 29 cm

Answer: B) 28 cm

Explanation: Scale factor = 123, so the side is 7 123 = 28 cm. SLO M-09-B-16 · Knowledge

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3. All circles are similar because:

  1. every circle is an enlargement of any other circle
  2. they have the same area
  3. they have the same radius
  4. they have no sides

Answer: A) every circle is an enlargement of any other circle

Explanation: Only the size (radius) changes, never the shape. SLO M-09-B-16 · Knowledge

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4. Are a 2 7 rectangle and a 6 21 rectangle similar?

  1. Yes, because 62 = 217 = 3
  2. No, because their perimeters differ
  3. It cannot be decided
  4. No, because all rectangles have right angles

Answer: A) Yes, because 62 = 217 = 3

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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5. Two similar figures have corresponding lengths in the ratio 1 : 2. Their areas are in the ratio:

  1. 1 : 8
  2. 2 : 4
  3. 1 : 4
  4. 1 : 2

Answer: C) 1 : 4

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

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6. If the radius of a sphere is tripled, its volume becomes:

  1. 9 times as large
  2. 3 times as large
  3. 6 times as large
  4. 27 times as large

Answer: D) 27 times as large

Explanation: Volume scales by 3^3 = 27. SLO M-09-B-17 · Understanding

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7. Two similar bottles have heights in the ratio 1 : 3. The smaller holds 15 ml. The larger holds:

  1. 135 ml
  2. 405 ml
  3. 420 ml
  4. 45 ml

Answer: B) 405 ml

Explanation: Volume ratio = 1 : 27, so the larger holds 15 27 = 405 ml. SLO M-09-B-17 · Understanding

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8. Two polygons are similar when:

  1. they have the same perimeter
  2. they have the same area
  3. corresponding angles are equal and corresponding sides are in the same ratio
  4. only their angles are equal

Answer: C) corresponding angles are equal and corresponding sides are in the same ratio

Explanation: Both conditions are needed for polygons (for triangles, equal angles are enough). SLO M-09-B-16 · Knowledge

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9. Two similar solids have lengths in the ratio 1 : 2. Their volumes are in the ratio:

  1. 1 : 4
  2. 1 : 6
  3. 1 : 2
  4. 1 : 8

Answer: D) 1 : 8

Explanation: Volumes scale by the cube: 2^3 = 8. SLO M-09-B-16 · Knowledge

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10. Which pair is not always similar?

  1. two circles
  2. two squares
  3. two equilateral triangles
  4. two rectangles

Answer: D) two rectangles

Explanation: A 1 2 rectangle and a 1 5 rectangle have different shapes. SLO M-09-B-16 · Knowledge

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11. A model building is made to a scale of 1 : 50. The model has a volume of 2000 cm³. The real building's volume is:

  1. 250 000 000 cm³ (250 m³)
  2. 100 000 cm³
  3. 5 000 000 cm³
  4. 40 cm³

Answer: A) 250 000 000 cm³ (250 m³)

Explanation: Volume scale = 50^3 = 125,000; 2000 125,000 = 250,000,000 cm³ = 250 m³. SLO M-09-B-17 · Understanding

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12. The areas of two similar triangles are in the ratio 4 : 9. Their corresponding sides are in the ratio:

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

Answer: D) 2 : 3

Explanation: Length ratio = 4 : 9 = 2 : 3. SLO M-09-B-17 · Understanding

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13. Two similar triangles: the first has sides 4 cm and 6 cm; the corresponding side to 4 cm in the second is 10 cm. The side corresponding to 6 cm is:

  1. 16 cm
  2. 12 cm
  3. 15 cm
  4. 203 cm

Answer: C) 15 cm

Explanation: Scale factor = 104, so the side is 6 104 = 15 cm. SLO M-09-B-16 · Knowledge

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14. Two similar solids have lengths in the ratio 1 : 3. Their volumes are in the ratio:

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

Answer: D) 1 : 27

Explanation: Volumes scale by the cube: 3^3 = 27. SLO M-09-B-16 · Knowledge

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15. A model car is made to a scale of 1 : 20. The model's paint covers 150 cm². The real car's painted area is:

  1. 1 200 000 cm²
  2. 60 000 cm² (6 m²)
  3. 3000 cm²
  4. 7.5 cm²

Answer: B) 60 000 cm² (6 m²)

Explanation: Area scale = 20^2 = 400; 150 400 = 60,000 cm². SLO M-09-B-17 · Understanding

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16. The volumes of two similar cones are in the ratio 27 : 125. Their surface areas are in the ratio:

  1. 27 : 125
  2. 9 : 25
  3. 3 : 5
  4. 729 : 15625

Answer: B) 9 : 25

Explanation: Length ratio = [3]27 : [3]125 = 3 : 5; area ratio = 9 : 25. SLO M-09-B-17 · Understanding

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17. Two similar figures have corresponding lengths in the ratio 3 : 7. Their areas are in the ratio:

  1. 9 : 49
  2. 3 : 7
  3. 27 : 343
  4. 6 : 14

Answer: A) 9 : 49

Explanation: Areas scale by the square of the length ratio: 3^2 : 7^2 = 9 : 49. SLO M-09-B-16 · Knowledge

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18. Are a 4 6 rectangle and a 6 9 rectangle similar?

  1. No, because all rectangles have right angles
  2. It cannot be decided
  3. No, because their perimeters differ
  4. Yes, because 64 = 96 = 32

Answer: D) Yes, because 64 = 96 = 32

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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19. A small pizza (diameter 20 cm) costs Rs. 500. A similar pizza of diameter 30 cm, priced by area, should cost:

  1. Rs. 1,125
  2. Rs. 1,687.50
  3. Rs. 1,000
  4. Rs. 750

Answer: A) Rs. 1,125

Explanation: Area factor = (30/20)^2 = 2.25; 500 2.25 = 1125. SLO M-09-B-17 · Understanding

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20. Two similar shapes have corresponding lengths in the ratio 1 : 3. The smaller has area 12 cm². The area of the larger is:

  1. 36 cm²
  2. 324 cm²
  3. 120 cm²
  4. 108 cm²

Answer: D) 108 cm²

Explanation: Area ratio = 1 : 9, so the larger area is 12 9 = 108 cm². SLO M-09-B-17 · Understanding

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21. Two similar figures have corresponding lengths in the ratio 2 : 5. Their areas are in the ratio:

  1. 2 : 5
  2. 4 : 10
  3. 4 : 25
  4. 8 : 125

Answer: C) 4 : 25

Explanation: Areas scale by the square of the length ratio: 2^2 : 5^2 = 4 : 25. SLO M-09-B-16 · Knowledge

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22. Two similar bottles have heights in the ratio 2 : 5. The smaller holds 16 ml. The larger holds:

  1. 266 ml
  2. 250 ml
  3. 100 ml
  4. 40 ml

Answer: B) 250 ml

Explanation: Volume ratio = 8 : 125, so the larger holds 16 1258 = 250 ml. SLO M-09-B-17 · Understanding

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23. Are a 5 8 rectangle and a 10 12 rectangle similar?

  1. Yes, because all rectangles have right angles
  2. Yes, because their perimeters differ
  3. No, because 105 neq 128
  4. It cannot be decided

Answer: C) No, because 105 neq 128

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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24. The areas of two similar triangles are in the ratio 1 : 49. Their corresponding sides are in the ratio:

  1. 1 : 24
  2. 1 : 49
  3. 1 : 7
  4. 1 : 343

Answer: C) 1 : 7

Explanation: Length ratio = 1 : 49 = 1 : 7. SLO M-09-B-17 · Understanding

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25. Two similar bottles have heights in the ratio 2 : 3. The smaller holds 8 ml. The larger holds:

  1. 18 ml
  2. 35 ml
  3. 27 ml
  4. 12 ml

Answer: C) 27 ml

Explanation: Volume ratio = 8 : 27, so the larger holds 8 278 = 27 ml. SLO M-09-B-17 · Understanding

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