NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.2 – Part 2

Different types of shapes also its volume and total surface area formulas

Different Types of Shapes

Different types of shapes also its volume and total surface area formulas

Q-4 The diameter of a roller is 84cm and its length is 120cm . It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2 .Solution:

  • The roller length is (h) =120cm=1.2m

  • The cylinder radius is =842cm=42cm=0.42m

  • Total no. of revolutions =500

    Distance covered by roller in one revolution

    • Curvedsurfacearea=2πrh

    • (2×227×0.42×1.2)m2 (π=227)

    • 3.168m2

Area of the playground

  • (500×3.168)m2 ( 500 complete revolutions to level a playground)

  • 1584m2

Q-5 A cylindrical pillar is 50cm in diameter and 3.5m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs12.50perm2 .Solution:

  • The pillar radius (r)=502cm=25cm=0.25m

  • The pillar height (h)=3.5m.

  • Painting rate =Rs12.50perm2

    Curved surface

    • 2πrh

    • (2×227×0.25×3.5)m2

    • 5.5m2

    Total cost of painting

  • (5.5×12.5) (Painting rate Rs12.50perm2 )

  • Rs68.75

Q-6 Curved surface area of a right circular cylinder is 4.4m2 . If the radius of the base of the cylinder is 0.7m , find its height.Solution:

  • The radius of the base r and the height of the cylinder h.

  • Area of a right circular cylinder is 4.4m2

Curved surface area

  • 2πrh=4.4m2

  • 2×227×0.7×h=4.4 (π=227)

  • h=4.42×227×0.7=1m

  • h=4.4×72×22×0.7

  • h=1m

Q-7 The inner diameter of a circular well is 3.5m . It is 10m deep. Find

  1. Its inner curved surface area,

  2. The cost of plastering this curved surface at the rate of Rs40perm2.

Solution:

Circular well radius (r)=3.52m=1.75m The well depth (h)=10m Plastering rate =Rs40perm2

  1. Curved surface

    • 2πrh

    • (2×227×1.75×10)m2

    • 110m2

  2. Cost of plastering = Rs(110×40)=Rs4400

Q-8 In a hot water heating system, there is a cylindrical pipe of length 28m and diameter 5cm . Find the total radiating surface in the system.Solution:

Formulas for surface area and volume of a cylinder

Surface Area and Volume of a Cylinder

Formulas for surface area and volume of a cylinder

  • The pipe radius (r)=52cm=2.5cm=0.025m

  • The pipe length (h)=282m=14m

Total radial surface or curved surface area of the pipe

  • 2πrh

  • (2×227×0.025×28)m2

  • 4.42

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