1. 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

2. 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

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

4. If the ratio of the volumes of two spheres is 27:8, what will be the ratio of their curved surface areas?

5. If the ratio of the total surface areas of two solid spheres is 1:4, what will be the ratio of their volumes? Calculate and write it down.

6. If the volumes of two cubes are in the ratio 64:27, then the ratio of their total surface areas will be 9:16.

7. 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

8. 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

9. If the ratio of the volumes of two cubes is 4:343, determine the ratio of their total surface areas.

10. If the volumes of two solid spheres are in the ratio 27:8, what will be the ratio of their curved surface areas?

(a) 1:2 (b) 9:4 (c) 1:8 (d) 1:16

11. Under the condition that no interest will be charged if the money is repaid within two years, three friends borrowed ₹6000, ₹8000, and ₹5000 respectively from a cooperative bank to jointly purchase four cycle rickshaws. After two years, after deducting all expenses, their total income amounted to ₹30,400. They divided this income in proportion to their capital contributions and then repaid their individual bank loans. Now, calculate how much money each person will have left in hand and what the ratio of the remaining amounts will be.

12. The ratio of the volumes of two spheres is 64:27. If the sum of their radii is 7 cm, what is the difference in their total surface areas?

13. The ratio of the volumes of two cubes is 4:125. What is the ratio of the surface areas of the two cubes?

(a) 2:5 (b) 4:25 (c) 4:5 (d) 2:25

14. 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

15. 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

16. 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

17. If the radii of two cones are in the ratio 2:3 and their heights are in the ratio 5:3, then what will be the ratio of their volumes?

(a) 4:9 (b) 9:4 (c) 27:20 (d) 20:27

18. If the ratio of the heights of two right circular cylinders is 1:2 and the ratio of their base circumferences is 3:4, then the ratio of their volumes will be 9:32.

19. Two friends start a partnership business by investing ₹40,000 and ₹50,000 respectively. They agree that 50% of the profit will be shared equally, and the remaining 50% will be divided in the ratio of their investments. If the first friend’s share of the profit is ₹800 less than the second friend’s share, then what is the first friend’s profit?

20. If the ratio of the heights of two right circular cones is 1:4 and the ratio of their radii is 2:1, then the ratio of their volumes will be ______.

21. If the volumes of two cones are in the ratio \(1:4\) and their radii are in the ratio \(4:5\), then what will be the ratio of their heights?

(a) 1:5 (b) 5:4 (c) 5:16 (d) None of the above

22. If the ratio of the total surface areas of two solid spheres is 1:4, what is the ratio of their volumes?

23. If the ratio of the radii of two solid right circular cones is 2:3 and the ratio of their heights is 5:3, then the ratio of their volumes will be 27:30.

24. 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

25. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:4, then their radius ratio will be—.

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

26. If the volume ratio of two cubes is 4:1, then their edge ratio will be?

(a) \(2:1\) (b) \(\sqrt2:1\) (c) \(2\sqrt2:1\) (d) none of the above

27. If the ratio of the radii of two right circular cylinders is 2:3 and the ratio of their heights is 5:6, what will be the ratio of their volumes?

28. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:2, then their radius ratio will be –?

29. 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

30. If the volumes of two solid spheres are in the ratio 1:8, what is the ratio of their curved surface areas?

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