Students and Teacher's Forum

Students and Teachers Forum

1. The curved surface area of the cylinder of diameter 14 cm is 1320 cm². Find the total surface area of the cylinder.

Given, Diameter of the cylinder (d) = 14 cm or, radius of the cylinder (r) = d2 = 7 cm Curved surface area of the cylinder (CSA) = 1320 cm2 .....

2. The circumference of the base of the cylindrical drum is 88 cm and the sum of the radius and the height is 25 cm. Find the total surface area and the volume of the cylinder.

Let r be the radius & h be the height of cylinder. Given, Circumference of base of cylindrical drum (C) = 88 cm Or, 2πr = 88 cm Or, 2⨉ 3.14 ⨉ r = 88 .....

3. A solid cylinder has a diameter of 7 cm and length 10 cm. It is cut into two halves by cutting vertically along the diameter. Find the total surface area of each half.

Given, Diameter of the solid cylinder (d) = 7 cm Radius of the cylinder (r) = d/2 = 7 cm/2 = 3.5 cm Length of the solid .....

4. The diameter of the base of the cylinder is 42cm and height is 30 cm, find the
(a) the area of the curved surface
(b) the total surface area
(c) volume of the cylinder.

Given, Diameter of the base of the cylinder (d) = 42 cm Radius of the base of the cylinder (r) = 21 cm Height of the cylinder (h) = 30 cm. We know, (i) Area of .....

5. Find the curved surface area, total surface area and volume of the given cylinder. (Fig. cylinder with circumference of base = 88 cm and height 15 cm)

Given, Circumference of the base (C) = 88 cm Or, 2πr = 88 cm where, r = radius of cylinder. Or, 2 ⨉3.14 ⨉ r = 88 cm Or, 6.28 .....

6. The volume of a spherical ball is 7,241.14 cm³. Find the cost of painting its surface at the rate of Rs. 5 per sq. metre.

Given, Volume of the sphere (V) = 7241.14 cm3 Let r be the radius of sphere. We know, Volume of sphere (V) = 4/3 πr3 Or, 7241.14 .....

7. A solid cylinder has a diameter of 14 cm and height 25 cm. If it is cut into two equal halves vertically along the diameter, find the total surface area of each half.

Given, Diameter of the solid cylinder (d) = 14 cm Radius of the cylinder (r) = 7 cm Length of the .....

8. Find total surface area of a cylinder having radius 4.2 cm and height 4.9 cm.

Given, Radius of cylinder (r) = 4.2cm Height (h) = 4.9cm Total srface area (TSA) = ? We know, T.S.A of cylinder = 2πr(r+h) .....

9. A cylindrical well of 7 m diameter at the base and 20 m deep is dug up. Find the cost of plastering the inner surface area of the well including the base if the rate of plastering is Rs. 5 per sq.

Given, Diameter of the cylinder (d) = 7 m Radius of the cylinder (r) = 3.5 m Depth of the cylinder (h) = 20 m. Now, Inner surface area including base (A) = .....

10. The area of the base of the cylinder is 616 cm2 and height is 15 cm, find the
(a) the area of the curved surface
(b) the total surface area
(c) volume of the cylinder.

Given, Height of cylinder = h = 15cm Area of the base of the cylinder (A) = 616 cm2 Or, πr2 = 616 cm2, where r is radius of cylinder. Or, 3.14 ⨉ r2 .....

11. The radius of the base of the cylinder is 7 and height is 14 cm, find the
(a) the area of the curved surface
(b) the total surface area
(c) volume of the cylinder.

Given, Radius of the base of the cylinder (r) = 7 cm Height of the cylinder (h) = 14 cm. We know, (i) Area of the curved surface of cylinder (CSA) = 2πrh .....

12. A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. The length of the entire capsule is 14 mm and diameter of the capsule is 5 mm. Find its surface area.

Given, Length of the capsule (H) = 14 mm Diameter of the capsule (d) = 5 mm Radius of the capsule (r) = d2 .....

13. An iron pipe is 280 cm long. If its internal diameter is 10 cm and the thickness of the iron is 2 cm, find the volume of iron in the pipe.

Given, Length of the iron pipe (h) = 280 cm Internal diameter of the iron pipe (d2) = 10 cm Internal radius of the iron pipe (r2) = 5 cm .....

14. Find the difference in total surface area of a cube whose side measures 50 cm and the cylinder whose radius and height measure 20 cm and 1 m respectively.

Given, Measure of side of the cube (l) = 50 cm We know, Total surface area of the cube (TSAcube) = 6l2 .....

15. Find the curved surface area, total surface area and volume of the given cylinder. (Fig. cylinder with area of base = 7546 cm² and height 63 cm)

Let r be the radius and h be the height. Given, Area of the base of cylinder (A) = 7546 cm2 Or, πr2 = 7456 cm2 Or, 3.14 ⨉ r2 = 7456 cm2 Or, r2 .....

16. A cylindrical water vessel of diameter 1.4 m holds 770 liters of water. Calculate the height and the curved surface area of the vessel. (1000 l = 1 cu. m)

Given, Diameter of the cylindrical vessel (d) = 1.4 m Radius of the cylindrical vessel (r) = d 2 = 0.7 m Capacity of the cylindrical vessel (V) = 770 .....

17. The volume of the cylindrical can is 1232 cm³ and its height is 8 cm. Find the radius of the cylinder.

Given, Volume of the cylindrical can (V) = 1232 cm3 Height of the cylindrical can (h) = 8 cm. We know, Volume of a cylinder (V) = πr2h Or, 1232 cm3 = 3.14 .....

18. The edge of a cube is 22 cm and the height of the cylinder 11 cm. If the area of the curved surface of a cylinder is equal to the total surface area of the cube, find the radius of the cylinder.

Given, Edge of the cube (l) = 22 cm Height of the cylinder (h) = 11 cm. According to the question, Area of curved surface of cylinder (CSA) = Total surface area of .....

19. A water vessel, cylindrical in shape of diameter 3.5 m, holds 770 liters of water. Find the total surface area of the cylindrical vessel.

Here, Diameter of the cylinder (d) = 3.5 m So , radius of the cylinder (r) = d2 = 1.75 m Capacity of the vessel (V) = 770 .....

20. The area of great circle of hemisphere is 5 cm². Find the curved surface area.

Given, Area of great circle(A) = πr2= 5cm2. CSA of hemi-sphere = ? We have, CSA of hemisphere= 2πr2 .....

21. The volume of a cylinder can is 1.54 liter. If the area of its base is 77 cm², find its height.

Here, Volume (V) = 1.54 liter=1.54 1000 cm3 = 1540 cm3 And, area of base(A) = 77 cm2 We have, Volume = Area of base ⨉ height Or, height = .....

22. The volume of a solid object formed by cutting a cylinder vertically along the diameter is 616 cm³. If the height of the solid object measures 8 cm, find the diameter along which it is cut.

Given, Volume of the solid object (V) = 616 cm3 Height of the solid object (h) = 8 cm We know, Volume of the half of cylinder (V) = 12πr2h Or, 616 cm3 = 2214 r2 ⨉ 8cm Or, r2 = 49 cm2 Or, r = √(49cm2 ) Or, r = 7 .....

23. Mohan made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath.

Given, Height of the cylinder (h) = 1.45 m = 1.45 ⨉ 100 cm .....

24. The external radius of a hollow spherical ball is 9 cm. If the volume of the ball is 2531.05 cm³, find the capacity of the ball.

Given, External radius of the spherical ball (R) = 9 cm Volume of the ball (V) = 2531.05 cm3. We know, Volume of the hollow sphere (V) = 43 π(R3 – r3) Or, .....

25. If the radius and slant height of the cone are r and l respectively. What will be the total surface area of a cone?

Here, Radius and slant height of the cone are r and l respectively. The total surface area of a cone is given by, TSA = curved surface area + area of circular .....

26. Find the total surface area of the cylinder whose diameter of the base is 70 cm and the height is 1 m.

Given, Diameter of the base of cylinder (d) = 70 cm Radius of the base of cylinder (r) = d2 = 35 cm Height of the cylinder (h) = 1 m = 100 cm. We know, Total .....

27. Find the curved surface area, total surface area and volume of the given cylinder. (Fig. cylinder with circumference of base = 132 cm and height 30 cm)

Given, Circumference of the base (C) = 132 cm Or, 2πr = 132 cm Or, 2 ⨉ 3.14 ⨉ r = 132 cm Or, 6.28 ⨉ r .....

28. Find the surface area and the volume of the sphere whose radius is 14 cm.

Given, Radius of the sphere (r) = 14 cm We know, Surface area of the sphere (TSA) = 4πr2 .....

29. Find curved surface area of a cylinder having diameter 10.5 cm and height 15.75 cm.

Given, Diameter = d = 10.5cm Height = h = 15.57cm Curved surface area = ? We have, CSA of cylinder = 2πrh = πdh .....

30. The circumference of the base of a cylinder is 88 cm. If the height of the cylinder is 12 cm, find the curved surface area of the cylinder.

Given, Height of the cylinder (h) = 12 cm Circumference of the base of cylinder (C) = 88 cm Or, 2πr = 88 cm, .....

31. The circumference of the base is 88 cm and the sum of its radius and height is 24 cm, find the total surface area of the following cylinder.

Here, we have given, Circumference of the base (C) = 2πr = 88cm Sum of radius and height (r+h) = 24cm. TSA of cylinder = ? Now, Total .....

32. 35 identical circular plates each of thickness 1 cm and radius 21 cm are placed one after another to form a right circular cylinder. Find the total surface area of the cylinder so formed.

Given, Total number of circular plates (N) = 35 Thickness of each plate (t) = 1 cm So, the height of the cylinder so formed (h) .....

33. The volume of a cylinder of height 10 cm is 3.85 cm³. Find the curved surface area and the total surface area of the cylinder.

Given, Height of the cylinder (h) = 10 cm Volume of the cylinder (V) = 3.85 cm3 We know, Volume of the cylinder (V) = πr2h Or, 3.85 cm3 .....

34. If the volume of the given solid object is 134.09 cm³, find its total surface area.

fig. A hemisphere with radius r

Here, Let r be the radius of hemi-sphere. Volume of the hemisphere (V) = 134.09 cm3 We know, Volume of the hemisphere (V) .....

35. If the volume of the given solid object is 56.57 cm³, find its total surface area.

(fig. A hemisphere with radius r)

Given, Volume of the hemisphere (V) = 50.307 cm3 Let r be the radius of hemi-sphere. We know, Volume of the hemisphere (V) = .....

36. The area of the base of a hemisphere is 452.57 cm². Find the total surface area, curved surface area and volume of the hemisphere.

(fig. A hemisphere with base area of 452.57 cm²)

Given, Area of the base of the hemisphere (A) = 452.57 cm2. Let r be the radius of hemi-sphere. We know, Area of base of a hemisphere (A) = .....

37. The curved surface area of a cylindrical drum is 176 cm². If the cylinder measures 16 cm in length, find the circumference of the base of the drum.

Given, Height of the cylinder (h) = 16 cm Curved surface area of cylinder (CSA) = 176 cm2 Or, 2πr ⨉ h = 176 cm2 Or, 2πr ⨉ 16 cm = 176 .....

38. A cylinder whose height is 7 cm has the total surface area of 18847 cm². Find the radius of the base of the cylinder.

Here, Height = h = 7cm The total surface area of the cylinder = TSA = 1884 7 cm2 . Let r be the radius of base. Then, TSA = 2πr2+2πrh Or, 18847 .....

39. The circumference of the great circular end of the hemisphere is 44 cm, find the total surface area and the volume of the hemisphere.

Given, Circumference of the great circle of the hemisphere (A) = 44 cm Or, 2πr = 44 cm where, r is .....

40. The given cone is fully filled with water. If the water is poured into the given cylindrical tank, upto what height does the water surface rise in the cylinder?

Here, Radius of cone (r) = 12 cm2= 6 cm Slant height (l) = 10 cm So, Height of cone (h) = √[l2 - r2] .....

41. The total height of the pencil shaped solid object given alongside is 30 cm. If the height of cone and cylinder are in the ratio of 2:3, find the volume of the solid object.

Let x be any constant. Since the height of the cone and cylinder are in the ratio 2:3, Height of cone = 2x Height of the cylinder = 3x According to the question, 2x + 3x = 30 Or, x = 6 cm So, Height of cone = 2x = 2 X 6 .....

42. The total surface area of the given hemisphere is 11,550 cm². Find its volume.

(fig. A hemisphere with radius r)

Given, Total surface area of hemisphere (TSA) = 11550 cm2. Let r be the radius of hemi-sphere. We know, Total surface area of hemisphere (TSA) = 3πr2 .....

43. Find the surface area of sphere having diameter 14 cm.

Given, Diameter (d) = 14cm. Surface area = ? We have, Surface area of sphere = πd2 .....

44. A sphere is divided into two equal parts of volume 4603.23 cm³ each. Find the surface area of the sphere before the division.

Given, Volume of the hemisphere (V) = 4603.23 cm3 We know, Volume of the hemisphere (V) = 23 πr3 Or, 4603.23 cm3 =23 ⨉ 227 ⨉ r3 Or, 4603.23 cm3 = .....

45. The radius of the base of a cylinder is 14 cm. If the height of the cylinder is 20 cm, find
a) the area of the curved surface
b) the total surface area
c) volume of the cylinder.

Given, Radius of the base (r) = 14 cm Height of the cylinder (h) = 20 cm We know, (i) Area of the curved surface of cylinder (CSA) = 2πrh .....

46. A sphere is divided into two equal parts of volume 8316 cm³ each.Find the total surface area of the sphere before the division.

Given, Volume of the hemisphere (V) = 8316 cm3 We know, Volume of the hemisphere (V) = 27 πr3 , r is radius of sphere. Or, 8316 cm3 = 23 ⨉ 227 ⨉ .....

47. The total surface area of a solid sphere made of earth is 201.14 cm². Two hemispheres are formed when it is cut into two equal parts. Find the total surface area of each hemisphere.

Let r be the radius of sphere. Given, Total surface area of the sphere (TSA) = 201.14 cm2 Or, 4πr2 = 201.14 cm2 or, πr2 = 50.285cm2. Again, Total .....

48. A pipe measures 12 cm in length. If the outer and inner radius of the pipe are 2 cm and 1 cm respectively, find the total surface area of the pipe.

Given, Length of the pipe (h) = 12 cm Outer radius of the pipe (r1) = 2 cm. Inner radius of the pipe (r2) = 1 cm. We know, Total surface area of the .....

49. The volume of a sphere is 33.52 cm³. Find the surface area of the sphere.

Let r be the radius of sphere. Given, Volume of the sphere (V) = 33.52 cm3 We know, Volume of sphere (V) = 43 πr3 Or, 33.52 cm3 = 43 ⨉ 227 ⨉ r3 Or, 33.52 cm3 = 8821 ⨉ r3 Or, 33.52 cm3 ⨉ .....

50. Three solid metallic sphere of radii 1, 6 and 8 cm respectively are melted to form a new solid sphere. Find the diameter of the new sphere.

Given, Radius of 1st sphere (r1) = 1 cm So, volume of 1st sphere (V1) = 43 πr13 .....