NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 2

Cylinder volume=πr^2 h

Cylinder Volume

Cylinder volume=πr^2 h

Q-3 A soft drink is available in two packs

  1. A tin can with a rectangular base of length 5cm and width 4cm , having a height of 15cm and

  2. A plastic cylinder with circular base of diameter 7cm and height 10cm

Which container has greater capacity and by how much?

Solution (i)

Capacity of tin can

  • l=5cm

  • b=4cm

  • h=15cm

Capacity =l×b×h

  • =5×4×15cm3

  • =300cm3

Solution (ii)

Capacity or volume of plastic cylinder is given as πr2h

Diameter =7cm , therefore radius(r) =72cm

Height (h) =10cm

Therefore, capacity =πr2h=227×(72)2×10=385cm3

Clearly the second container, the plastic cylinder has greater capacity than the first container, a tin can. The cylinder has 385380=5cm3 more volume.

Q-4 If the lateral surface of a cylinder is 94.2cm2 and its height is 5cm ,and then find

  1. Radius of its base

  2. Its volume .( useπ=3.14 )

Solution:

  1. Consider the radius of the cylinder be rcm.

    Height =5cm

    • Later surface area =94.2cm2=2πrh

    • 2×3.14×r×5=94.2

    • r=94.22×3.14×5

    • r=94.231.4

    • r=3cm

    So, the radius of the base is 3cm.

  2. Now, volume of cylinder =πr2h

  • =3.14×3×3×5cm3

  • =141.3cm3

Q-5 It costs Rs2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs20perm2, find

  1. Inner curved surface area of the vessel

  2. Radius of the base

  3. Capacity of the vessel

Solution:

  1. Inner curved surface area of the vessel

    • TotalcostofpaintingRateofpainting

    • =220020m2

    • =110m2

  2. Radius of the base

    • Consider the radius of the base r

    • The height of the cylindrical vessel h=10m

    We know that inner curved surface area =110m2

    • Therefore, 2πrh=110m2

    • 2×227r×10=110

    • r=110×72×22×10

    • r=770440

    • r=1.75m

    So, the radius of the base is 1.75m

  3. Capacity of the vessel =πr2h

  • =227×1.75×1.75×10m3

  • =673.757

  • =96.25m3

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