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 Equation is Equation liters. How many square meters of metal sheet would be needed to make it?

Solution:

  • Consider the radius of the cylinder to be Equation

  • Height(h) of cylindrical vessel is Equation

  • Since 1 cubic meter = 1000 liter. Therefore, volume of cylindrical vessel Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

    • Equation

So, the radius of the base of vessel Equation

Total surface area of the cylindrical vessel

  • Equation

  • Equation

  • Equation

  • Equation

  • Equation

So, Equation 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 Equation and the diameter of the graphite is Equation . If the length of the pencil is Equation , 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 Equation

  • Radius Equation Equation

  • Length of graphite Equation

Volume of the graphite cylinder Equation

  • Equation

  • Equation

Diameter of the pencil Equation

  • Therefore, radius Equation Equation

  • Length of pencil Equation

Volume of the pencil Equation

  • Equation

  • Equation

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

  • Equation

  • Equation

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

Solution:

  • Diameter of the cylindrical bowl Equation

  • Therefore, radius Equation Equation

  • Height of serving bowl Equation

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

  • Equation

  • Equation

  • Equation

Volume of soup given to Equation patients

  • Equation

  • Equation

  • Equation Liters ( 1 liter = 1000 cubic centimeter)

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