1. If the ratio of the lengths of two corresponding sides of two similar triangles is 7:11, then the ratio of their perimeters is —

(a) 11:7 (b) 49:121 (c) 7:11 (d) 121:49

2. If the ratio of the lengths of two corresponding sides of two similar triangles is 7:11, then their perimeter ratio is _____.

3. If the bases of two triangles lie on the same straight line and the other vertex of both triangles is common, then the ratio of their areas is ______to the ratio of the lengths of their bases.

4. If two triangles are equiangular (have equal corresponding angles), then the ratios of their corresponding sides will be equal; that is, their corresponding sides will be proportional.

5. If two triangles have their bases on the same straight line and share the same vertex (the opposite vertex), then the ratio of their areas is equal to the ratio of the lengths of their bases.

6. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

7. If the diameters of two cones are equal and the ratio of their slant heights is 5:7, then what is the ratio of their curved surface areas?

(a) 25:7 (b) 25:49 (c) 5:49 (d) 5:7

8. If the ratio of the volumes of two cubes is 8:27, then what will be the ratio of their total surface areas?

9. If the ratio of the curved surface areas of two spheres is 1 : 4, find the ratio of their volumes.

10. If the ratio of the volumes of two cubes is 1:27, then the ratio of their total surface areas will be —

(a) 1:3 (b) 1:8 (c) 1:9 (d) 1:18

11. The volume of a cone is jointly proportional to the square of the radius of the base and its height. If the ratio of the radii of two cones is 2:3 and their heights are in the ratio 5:4, then find the ratio of their volumes.

12. If the ratio of the volumes of two solid spheres is 1:27, then what is the ratio of their curved surface areas?

(a) 1:9 (b) 1:4 (c) 1:3 (d) 1:2

13. If the ratio of the curved surface areas of two solid spheres is \(1:9\), then their volume ratio will be?

(a) 1:3 (b) 1:27 (c) 1:81 (d) 1:243

14. If the volume ratio of two solid spheres is 1:8, find the ratio of their curved surface areas.

(a) 1:2 (b) 1:4 (c) 1:8 (d) 1:16

15. If the ratio of the volumes of two cubes is 1:27, then the ratio of their total surface areas will be _____.

16. If the ratio of the volumes of two solid spheres is 1:8, then the ratio of their curved surface areas is 1:4.

17. If the ratio of the radii of two tall solid circular cones is 2:3 and the ratio of their heights is 5:3, then what is the ratio of their curved surface areas?

(a) 8:07 (b) 2:05 (c) 10:09 (d) 16:09

18. If the ratio of the heights of two right circular cylinders is 1:2, and the ratio of the perimeters (circumferences) of their bases is 3:4, then find the ratio of their volumes.

19. If the ratio of the volumes of two cubes is 1:27, then what is the ratio of their total surface areas?

(a) 1:3 (b) 1:8 (c) 1:9 (d) 1:18

20. The ratio of the radii of two right circular solid cylinders is 2:3, and the ratio of their heights is 5:3. Find the ratio of their curved surface areas.

21. If the volumes of two right circular solid cylinders are equal and the ratio of their heights is 1:2, then find the ratio of their radii.

(a) 1:\(\sqrt2\) (b) \(\sqrt2\):1 (c) 1:2 (d) 2:1

22. If the ratio of the curved surface areas of two hemispheres is 4:9, then the ratio of their radii will be 2:3.

23. The perimeters of two similar triangles are 27 cm and 16 cm respectively. If one side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle.

24. If the ratio of the radii of two vertical solid cylinders is 2:3 and the ratio of their heights is 5:3, then the ratio of their curved surface areas is 20:27.

25. The volumes of two perpendicular circular rings are equal. The ratio of their heights is 4:9, then what will be the ratio of their radii?

(a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

26. The volume ratio of two solid spheres is 4:27. The ratio of their curved surface areas is-

(a) 4:9 (b) 2:3 (c) 16:35 (d) 8:27

27. If the volume ratio of two solid spheres is 1:8, the ratio of their curved surface areas will be -

(a) 1:2 (b) 2:1 (c) 1:4 (d) 1:16

28. If the volumes of two cones are in the ratio 1:4 and the ratio of the diameters of their bases is 4:5, find the ratio of their heights

(a) 1:5 (b) 5:4 (c) 5:16 (d) 25:64

29. If the profit-sharing ratio of two friends in a partnership business is \(\cfrac{1}{2}:\cfrac{1}{3}\), then their capital ratio is—?

(a) 2 : 3 (b) 3:2 (c) 1:1 (d) 5:3

30. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?

(a) 1:3 (b) 2:3 (c) 3:2 (d) 3:1