Solution: Let radius of outer shell = R & inner shell radius = r If the cylinder is made up of volume 99 cm 3 metal. = 2 x ( 22/7) x ( 12.5 + 11.5 ) x ( 20 + 1) = 3168 cm 2Įxample-5: The height of a metallic hallow cylinder is 14 cm and difference between its inner curved surface area and outer curved surface area is 44 cm 2. Total surface area of the pipe = 2 π ( R + r) (h + R – r) Inner shell radius = r = 12.5 – 1 = 11.5 cm Solution: Here radius of outer shell = R = 25/2 = 12.5 cm I.e Lateral surface area of the garden roller = π D h = (22/7) x 0.7 x 2 = 4.4 m 2Įxample-4: A hollow pipe long 20 cm, outer dia is 25 cm and thickness of the metal 1 cm. Here dia of roller (D)= 0.7 m and long (h) = 2 m Solution: Garden roller covered in one revolution = Curved Surface Area of roller Then find area covered by it in 10 revolution. ⇒ 15 x (4/3) x π x r 3 = π x (10) 2 x 5.4Įxample-3: The diameter of a garden roller is 0.7 m and it is 2 m long. Total volume of spheres = Volume of resultant cylinder Solution: Let the radius of cylinder = r, ThenĮxample-2 : 15 number of identical spheres are melted and converted into cylinder shape of 10 cm radius and 5.4 cm height is made. Volume of the material for hollow cylinder = π R 2 h – π r 2 h = π h ( R 2 – r 2 ) Examples on surface area and volume calculation of cylinderĮxample-1 : In a cylinder volume (v) = 176 cm 3, h = 14 cm, then find the radius of cylinder
Volume of the material used for hollow cylinder = Volume of the cylinder with outer radius – Volume of the cylinder with inner radius Total surface area hollow cylinder = 2 π ( R + r) (h + R – r) Total surface area hollow cylinder = Outer surface area of the cylinder + Inner surface area of cylinder + Area of a base circular ring + Area of a top circular ring Its dimensions are defined in the form of the radius of the base outer ( R), Inner ( r) & height ( h) Surface Area & Volume of a hollow cylinderĬurved Surface of hollow cylinder = Outer surface area of the cylinder + Inner surface area of cylinderĬurved Surface of hollow cylinder = 2 π h ( R + r) I.e A Hollow cylinder can be defined as, It is a solid bounded by two co-axial cylinders of the same height Volume of a Oblique Cylinder = π r 2 h = π r 2 a sin x Hollow CylinderĪ hollow cylinder is the figure in shape formed by just the lateral surface of the cylinder. Volume of Oblique Cylinder is the same as for the Right circular cylinder
Total Surface Area of Cylinder = 2 π r ( r + a) Total Surface Area of Oblique cylinder ( A s )
Lateral or Curved surface area of a Oblique Cylinder ( A a ) Perpendicular height of a Oblique Cylinder Its dimensions are defined in the form of the radius of the base ( r) and lateral height or perpendicular height or altitude ( h), Slant height ( a), angle ( x) Surface Area & Volume of an oblique cylinder The cylinder is sideways and the axis is not a right angle to the base, then it is called an oblique cylinder. Volume of a Cylinder = π r 2 h Oblique CylinderĪ The line joining the centers of the circular bases. Volume of a cylinder = Area of the circular base X height = π r 2 X h
Total Surface Area of Cylinder = 2 π r ( r + h) Total surface area of the right circular cylinder = Curved Surface Area of Cylinder + Base area + Top areaīase area = Top area = Area of the circle with same radius = π r 2 Perimeter of the base of the cylinder = Perimeter of circle with same radius = 2 π rĬurved Surface Area of Cylinder = 2 π r h Surface Area & Volume of a Right circular cylinderĬurved surface area of the right circular cylinder = Perimeter of the base of the cylinder X height I.e The lateral surfaces are curved and ends are congruent circlesĪ The line joining the centers of the circular bases is perpendicular to base, solid figure is called right circular cylinder. Its dimensions are defined in the form of the radius of the base (r) and height ( h).
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