1. If the numerical value of the volume of a right circular cone is equal to the numerical value of its curved surface area, what is the radius of the cone?

2. The numerical value of the volume of a cube is equal to the numerical value of the sum of its edges. The total surface area of the cube is - -

(a) 12 square unit (b) 36 square unit (c) 72 square unit (d) 144 square unit

3. The volume of a right rectangular prism is 960 cubic centimeters. If the ratio of its length, width, and height is 6:5:4, what is the total surface area of the prism?

(a) 590 square cm (b) 592 square cm (c) 295 square cm (d) 596 square cm

4. The length of a right rectangular prism is three times its width and five times its height. If its volume is 14,400 cubic centimeters, then what is its total surface area?

(a) 4300 square cm (b) 4320 square cm (c) 4500 square cm (d) 4520 square cm

5. If the total surface area of a cube is 216 square centimeters, what is its volume?

(a) 216 tcubic cm (b) 212 cubic cm (c) 316 cubic cm (d) 256

6. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?

(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm

7. The diagonal of a cuboid is √725 cm and its volume is 3000 cubic cm. The total surface area of the cuboid is 1300 square cm. Find the length, breadth, and height of the cuboid.

8. A solid vertical cylindrical cone has both its diameter and height equal to 21 cm. Find the volume of the largest possible sphere that can be obtained from this cone. Also, determine the ratio of the volumes of the cone and the sphere.

9. Here’s the English translation of your sentence: "A right rectangular prism has its length twice the breadth and its height half the breadth. If the total surface area of the prism is 448 square centimeters, find its volume."

10. If the side length of a cube is equal to the radius of a sphere, then which one has the greater volume?

11. The radius of the base of a solid right circular cone is equal to the radius of a solid sphere. If the volume of the sphere is twice the volume of the cone, find the ratio of the height of the cone to the radius of its base.

12. A solid sphere and a solid cone have the same diameter, and their total surface areas are equal. What is the ratio of the cone's height to its diameter?

13. The length, breadth, and height of a cuboid are in the ratio 4:3:2. If its total surface area is 468 square meters, find the volume of the cuboid.

14. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) will be –

(a) \(s=6d^2\) (b) \(3s=7d\) (c) \(s^3=d^2\) (d) \(d^2 = \cfrac{s}{2}\)

15. The total surface area of a right square prism is equal to half the square of its diagonal. Show that the prism is a cube.

16. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) is \[ s = 6d^2 \]

17. If the total surface area and the volume of a cube are numerically equal, then the length of its edge will be -- units.

18. A rectangular sheet of paper has length \(l\) units and width \(b\) units. When rolled along its length, it forms a cylindrical tube whose circumference is equal to the length of the paper. The curved surface area of the cylinder is ___ square units.

19. If the curved surface area of a solid sphere is numerically equal to three times its volume, then the numerical value of the diameter of the sphere is —.

(a) 1 units (b) 2 units (c) 3 units (d) 4 units

20. If the length of a cube's diagonal is \(4\sqrt{3}\) cm, determine its total surface area.

21. A solid cuboid has a length, width, and height ratio of \(4:3:2\), and its total surface area is \(468\) square cm. Determine the volume of the cuboid.

22. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) is \(s^3 = d^2\).

23. If the area of one face of a cube is 16 square centimeters, determine its volume.

24. The surface area of a sphere is equal in square units to twice its volume in cubic units. Find the radius of the sphere.

25. If the numerical values of the volume and lateral surface area of a cone are equal, then the relationship between its height and base radius is?

(a) \(r^2-h^2=2^2\) (b) \(2r^2+h^2=3^2\) (c) \(r^2+h^2=3^2\) (d) none of the above

26. If the total length of the edges of a solid cube is 36 cm, then its volume will be –?

(a) 9 cubic cm (b) 54 cubic cm (c) 27 cubic cm (d) 36 cubic cm

27. A rectangle has a length of \( a \) units and a breadth of \( b \) units. When the rectangle is wrapped to form a right circular cylinder, the circumference of the base of the cylinder is equal to the length of the rectangle. The lateral surface area of the cylinder will be _____.

28. The lateral surface area of a right circular cylinder is equal to its volume. Determine the base area of the cylinder.

29. A rectangular sheet of paper has a length of \(l\) units and a breadth of \(b\) units. The sheet is rolled to form a right circular cylinder, where the circumference equals the length of the paper. The curved surface area of the cylinder is ____ square units.

30. A solid object has its lower part in the shape of a hemisphere and its upper part in the shape of a right circular cone. If the surface areas of both parts are equal, determine the ratio of the radius to the height of the cone.