NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.6 – Part 3

Formulas for volume of common solids

Volumes of Common Solids

Formulas for volume of common solids

Q-6 The capacity of a closed cylindrical vessel of height 1m is 15.4 liters. How many square meters of metal sheet would be needed to make it?

Solution:

  • Consider the radius of the cylinder to be r

  • Height(h) of cylindrical vessel is 1m

  • Since 1 cubic meter = 1000 liter. Therefore, volume of cylindrical vessel =15.4liters=0.0154m3

    • πr2h=0.0154

    • (227×r2×1)m=(0.0154)m3

    • r2=0.0154×722

    • r2=0.107822

    • r2=0.0049

    • r=0.0049

    • r=0.07

So, the radius of the base of vessel =0.07m

Total surface area of the cylindrical vessel

  • =2πr(h+r)

  • =2×227×0.07(1+0.07)

  • =2×227×0.07(1.07)

  • =3.29567

  • =0.4708m2

So, 0.4708m2 of the metal sheet would be required to make the cylindrical vessel.

Q-7 A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7mm and the diameter of the graphite is 1mm . If the length of the pencil is 14cm , find the volume of the wood and that of the graphite.

Solution:

Ellipse c Ellipse c: Ellipse with foci A, A_1 passing through C Ellipse c_1 Ellipse c_1: Ellipse with foci A_2, A_3 passing through C_1 Segment f Segment f: Segment [A, B] Segment f_1 Segment f_1: Segment [A_1, B_1] Segment g Segment g: Segment [D, E] Vector u Vector u: Vector[F, G] Vector u Vector u: Vector[F, G] Vector v Vector v: Vector[H, I] Vector v Vector v: Vector[H, I] Vector w Vector w: Vector[J, K] Vector w Vector w: Vector[J, K] Vector a Vector a: Vector[L, M] Vector a Vector a: Vector[L, M] Vector b Vector b: Vector[N, O] Vector b Vector b: Vector[N, O] Vector d Vector d: Vector[P, Q] Vector d Vector d: Vector[P, Q] 7 mm text1 = "7 mm" 14 cm text2 = "14 cm" 1 mm text3 = "1 mm"

Cylinder of Wood

Cylinder of wood with solid cylinder of graphite filled in the interior.

  • Diameter of the graphite cylinder =1mm=110cm

  • Radius =120cm (radius=diameter2)

  • Length of graphite =14cm

Volume of the graphite cylinder =πr2h

  • =(227×120×120×14)cm3

  • =0.11cm3

Diameter of the pencil =7mm=710cm

  • Therefore, radius =720cm (radius=diameter2)

  • Length of pencil =14cm

Volume of the pencil =πr2h

  • (227×720×720×14)cm3

  • 5.39cm2

Now pencil has wood and graphite, therefore volume of wood = volume of the pencil - volume of the graphite

  • (5.390.11)cm3

  • 5.28cm3

Q-8 A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7cm . If the bowl is filled with soup to a height of 4cm , how much soup the hospital has to prepare daily to serve 250 patients?

Solution:

  • Diameter of the cylindrical bowl =7cm

  • Therefore, radius =72cm (radius=diameter2)

  • Height of serving bowl =4cm

So, soup saved in one serving = volume of the bowl

  • =πr2h

  • =(227×72×72×4)cm3

  • =154cm3

Volume of soup given to 250 patients

  • =(250×154)cm3

  • =38500cm3

  • =38.5 Liters ( 1 liter = 1000 cubic centimeter)

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