NTSE Mathematics Mensuration Online Test Set B

1. The diameter of circular wheel is 14 cm. How many revaluations will it make in moving 5.28 km ?

2. The ratio a canal, 30 dm wide and 12 dm deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes, if 8 cm of standing water is required for irrigation.

3. The outer measurements of a closed wooden box are 42 cm, 30 cm and 27 cm. If the box is made of 1 cm thick wood, determine the capacity of the box.

4. How many meters of cloth of 1.1 m width be required to make a conical tent whose vertical height is 12 m and base radius is 16 m ? Find also the cost of the cloth used at the rate of Rs. 14 per meter.

5. The base radius of solid in the form of a cone is 4 cm and the height of the cone is 9 cm. it is melted and recast into spherical balls of radius 0.5 cm. Find the number of balls, thus obtained.

6. A hemispherical tank of radiusis full of water. it is connected with a pipe which empties it at the rate of 7 liters per second. How mush time will it take to empty the tank completely ?

7. How many balls, each of radius 2 cm, can be made from a solid sphere of lead of radius 16 cm ?

8. In the radii of the ends of a bucket, 45 cm high are 28 cm, and 7 cm, determine its surface area.

9. A solid is in the form of a right circular cylinder with a hemisphere at one end and cone at the other end. Their common diameter is 4.5 cm and the height of the cylindrical and conical portions are respectively 1 cm and 8 cm. Taking ¹= 3.14. Find the cost of polishing the surface of the entire solid at the rate of Rs. 150 per cm2.

10. The shape of a solid is a cylinder surmounted by a cone. If the volume of the solid is 40656 cm3, the diameter of the base is 42 cm and the height of the cylinder is 20 cm, find the slant height of the conical portion.

11. An iron rod of length 1 m and diameter 4 cm is melted and cast into thin wires of length 20 cm each. If the number of such wires be 2000, find the radius of each thin wire.

12. If the diameter of the cross-section of a wire is decreased by 5%, how mush percent will the length be increased so that the volume remains the same ?

13. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

14. The height of a right circular cylinder is equal to its diameter. If it is melted and recast into a sphere of radius equal to the radius of the cylinder, find the part of the material that remained unused.

15. The area of a regular hexagon of side 8 cm is

16. A sphere of radius 3 cms is dropped into a cylindrical vessel of radium 4 cms. If the sphere is submerged completely, then the height (in cm) to which the water rises, is

17. A cone and cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is 3m, then the slant height of the cone (in m) is

18. If each side of rectangle is increased by 50%, then its area will be increased by

19. There is cylinder circumscribing the hemisphere such that their bases are common. The ratio of their volume is

20. Inside a triangular garden there is a flower bed in the form of a similar triangle. Around the flower bed runs a uniform path of such a width that the side of the garden are double of the corresponding sides of the flower bed. The areas of the path and the flower bed are in the ratio :

21. The height of conical tent at the center is 5m. The distance of any point on its circular base from the top of the tent is 13m. The are of the slant surface is :

22. The area of the shaded portion in the given figure is :

23. The area of the shaded region in the given figure is :

24. The perimeter of the following shaded portion of the figure is :

25. In an isosceles triangle ABC (AB = AC) the altitude to the base and to a lateral side are equal to 10 cm and 12 cm respectively. The length of the base is

26. The length of four sides and a diagonal of the given quadrilateral are indicated in the diagram. If A denotes the area then A is

27. The area of 4 walls of the hall whose breadth is 15 m and height is 8 m is 1,068 sq. m., the length of the hall is

28. The dimensions of a brick are 24 cm x 12 cm x 8 cm. How many bricks will be required to build a wall 24 m x 8 m x 6 m if 20% of the walls is filled with mortar ?

29. Three cubes of metal, of edges 6 cm, 8 cm and 10 cm are melted to form a new cube. Find the diagonal of this cube.