9th class Math, Chapter 9: Similar Figures MCQs

1. If two polygons are similar, then:

1. (A) their corresponding angles are equal ✓
2. (B) their areas are equal
3. (C) their volumes are equal
4. (D) their corresponding sides are equal

2. The ratio of the areas of two similar polygons is:

1. (A) equal to the ratio of their perimeters
2. (B) equal to the square of the ratio of their corresponding sides ✓
3. (C) equal to the cube of the ratio of their corresponding sides
4. (D) equal to the sum of their corresponding sides

3. If the volumes of two similar solids are 125 cm³ and 27 cm³, the ratio of their corresponding heights is:

1. (A) 3:5
2. (B) 5:3 ✓
3. (C) 25:9
4. (D) 9:25

4. The exterior angle of a regular pentagon is:

1. (A) 40°
2. (B) 45°
3. (C) 60°
4. (D) 72° ✓

5. A parallelogram has an area of 64 cm² and a similar parallelogram has an area of 144 cm². If a side of the smaller parallelogram is 8 cm, the corresponding side of the larger parallelogram is:

1. (A) 10 cm
2. (B) 12 cm ✓
3. (C) 18 cm
4. (D) 16 cm

6. The total number of diagonals in a polygon with 9 sides is:

1. (A) 18
2. (B) 21
3. (C) 25
4. (D) 27 ✓

7. Two spheres are similar and their radii are in the ratio 4:5. If the surface area of the larger sphere is 500π cm², what is the surface area of the smaller sphere?

1. (A) 256π cm²
2. (B) 320π cm² ✓
3. (C) 400π cm²
4. (D) 405π cm²

8. A regular polygon has an exterior angle of 30°. How many diagonals does the polygon have?

1. (A) 54 ✓
2. (B) 90
3. (C) 72
4. (D) 108

9. In a regular hexagon, the ratio of the length of a diagonal (the longest) to the side length is:

1. (A) √3 : 1
2. (B) 2 : 1 ✓
3. (C) 3 : 2
4. (D) 2 : 3

10. A regular polygon has an interior angle of 165°. How many sides does it have?

1. (A) 15
2. (B) 16
3. (C) 20
4. (D) 24 ✓

11. Two polygons are similar if their corresponding angles are equal and their corresponding sides are:

1. (A) perpendicular
2. (B) proportional ✓
3. (C) equal
4. (D) parallel

12. Two triangles are similar if their corresponding angles are:

1. (A) supplementary
2. (B) complementary
3. (C) double
4. (D) equal ✓

13. Two triangles are similar if the ratios of all the corresponding sides are:

1. (A) equal ✓
2. (B) zero
3. (C) unequal
4. (D) integers

14. All circles are:

1. (A) similar ✓
2. (B) congruent
3. (C) equal in area
4. (D) not similar

15. Which of the following figures are always similar?

1. (A) two squares ✓
2. (B) two rectangles
3. (C) two rhombuses
4. (D) two parallelograms

16. If corresponding sides of two similar triangles are in the ratio 2:3, their corresponding angles are in the ratio:

1. (A) 2:3
2. (B) 4:9
3. (C) 3:2
4. (D) 1:1 ✓

17. If the ratio of corresponding lengths of two similar figures is k, the ratio of their areas is:

1. (A) k³
2. (B) 2k
3. (C) k² ✓
4. (D) k

18. If the lengths of similar figures are in the ratio 2:5, their areas are in the ratio:

1. (A) 2:5
2. (B) 8:125
3. (C) 5:2
4. (D) 4:25 ✓

19. If the ratio of corresponding lengths of two similar solids is k, the ratio of their volumes is:

1. (A) k²
2. (B) 3k
3. (C) k³ ✓
4. (D) k

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

1. (A) 16:81
2. (B) 4:9 ✓
3. (C) 2:3
4. (D) 8:27