Revision ASSGM-CLASS-IX (MENSURATION) PREPARED BY INDERJIT BHATIA-PCC

2. How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter.

3. Two cubes each with 12 cm edge are joined end to end. Find the surface area of the resulting cuboid.

4. Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

5. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.

6. Write all the formulae used in the chapters:à Areas related to Circles and Surface area & Volume.

7. Two circles touch internally, the sum of their areas is 116p sq. cm. and the distance between their centres is 6 cm. Find the radii of the circles.

8. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

9. A shuttle cock used for playing badminton has the shape of a frustum of a cone surmounted on a hemisphere. The external diameters of the frustum are 5 cm and 2 cm, the height of the entire shuttle cock is 7 cm. Find the external surface area.

10. A cone is divided into two parts by drawing a plane through the mid – point of its axis, parallel to its base. Compare the volumes of the two parts.

11. Solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the number of solid spheres dropped in the water.

12. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2.Find the diameter of the base of the cylinder.

13. Curved surface area of a cone is 308 cm2 and its slant height is 14 cm .Find adius of the base and total surfacel area of cone

14. A cuboidal water tank is 6m long 5m wide and 4.5m deep.How many litres of water can it hold.

15. A solid composed of a cylinder with hemi spherical ends.The whole height of the solid is 19cm and the radius of the cylinder is 3.5cm.Find the weight of the solid if 1cm3 of the metal weighs 4.5g.

16. Find the volume of a sphere whose area is 154 cm2.

17. A hemispherical tank is made up of an iron sheet 1 cm thick.If the inner radius is 1m,then find the volume of iron used to make the tank

18. The total surface area of right circular cylinder is 231cm2. If its curved surface area is ⅔ of its total surface, determine its radius and height.

19. A closed box is made of wood which is 1cm thick. The external dimensions of the box are 1.5m, 1.08m and 0.72m, find the Volume of the wood used in making the box.Capacity of the box

20. A conical tent is 12m high and 14m in diameter. find the area of canvas required to make it.Suppose if a person requires 5m2 space on ground and 12m3 in air, how many person such tent can accommodate

21. The volume of a right circular cone is 100π cm3 and its height is 12cm. Then its curved surface area is (a)62π cm2 (b)64π cm2 (c)65π cm2 (d)67π cm2

22. The radius and slant height of a cone are in the ratio 3:5.If its curved surface area is 135 π cm2, find its radius?

23. A Green house has dimensions 6m×4.5m×4m.It is made entirely of a glass panes (including base) held together with tape. (A) Find Area of the glass used,Length of tape required.(B) ,Cost of glass used at the rate of Rs45 per m2(C) ,Cost of tape used as the rate of Rs.3.50

24. One hundred and twenty five solid iron spheres ,each of radius r and surface area S are melted to form a solid sphere with surface area S/ .Find the : a)Radius r/ of new sphere b)Ratio S and S/

25. The Volume of the two sphere are in the ratio 64:27.Find the ratio of their surface area.

26. . The radius and height of a cone are in the ratio 4 : 3. The area of the base is 154 cm2. Find the area of the curved surface

27. . A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

28. A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder is 1.4 m. and its length is 5m. What will be the cost of painting it on the outside at the rate of Rs.10 per square metre.

29. A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm and if its height is 72 cm, find the uniform thickness of the cylinder.

30. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100 cm2.

31. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

32. Curved surface area of a right circular cylindrical is 4.4m2. If the radius of the base of the cylinder is 0.7m. Find its height

33. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100 cm2.

34. A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

35. A solid cube of side 24 cm is cut into 27 cubes of equal volume. What will be the side of the new cube

36. The inner diameter of the cylinder is 35cm and its outer diameter is 42cm. If its height is one metre, find the total surface area of the cylinder. If the radius and height of the cylinder, a cone and a hemisphere are same,

37. find the ratio of their volumes If every side of cube is doubled, its volume will become (a) twice (b) four times (c) eight times (d) thrice

38. A tank 10m × 5m
× 6m is full of water. How much water must be taken out to reduce the water
level by 1m (a) 30m^{2 }(b) 100m^{3} (c) 50m^{2} (d) none of
these

39. The total
surface area of right circular cylinder is 231cm^{2}. If its curved
surface area is ⅔ of its total surface, determine its radius and height

40. Slant height of a cone is & base diameter is , then height of the cone is (A) (B) (C) (D)

41. A cuboidal water tank is long, wide & deep. How many litres of water can it hold?

42. The capacity of a closed cylindrical vessel of height is How many square meter of metal sheet would be needed to make it

43. SA village having a population of , requires of water per head per day. It has a tank measuring For how much days will the water of this tank last

44. The C.S.A. of a
Cylinder is 4620 cm^{2}. Find its radius if height is 35 cm.

45. A closed box is made of wood which is 1cm thick. The external dimensions of the box are 1.5m, 1.08m and 0.72m, find the Volume of the wood used in making the box. & Capacity of the boxA conical tent is 12m high and 14m in diameter.

46. Find the area of canvas required to make it.Suppose if a person requires 5m2 space on ground and 12m3 in air, how many person such tent can accommodate.

47. A conical tent is 12m high and 14m in diameter. find the area of canvas required to make it.

Suppose if a person requires 5m2 space on ground and 12m3 in air, how many person such tent can accommodate.

48 A closed box is made of wood which is 1cm thick. The external dimensions of the box are 1.5m, 1.08m and 0.72m, find theVolume of the wood used in making the box.Capacity of the box

49) A closed box is made of wood which is 1cm thick. The external dimensions of the box are 1.5m, 1.08m and 0.72m, find the Volume of the wood used in making the box.& Capacity of the box.

50)A
conical tent is 12m high and 14m in diameter. find the area of canvas required
to make it. Suppose
if a person requires 5m^{2} space on ground and 12m^{3} in air,
how many person such tent can accommodate.

51) A solid cube of side 24 cm is cut into 27 cubes of equal volume. What will be the side of the new cube

52) A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl

53) The
radius and height of a cone are in the ratio 4 : 3. The area of the base is 154
cm^{2}. Find the area of the
curved surface.

54)A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder is 1.4 m. and its length is 5m. What will be the cost of painting it on the outside at the rate of Rs.10 per square metre. PREPARED BY INDERJEET BHATIA-PCC

(PREPARED BY INDERJEET BHATIA-PCC)