NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.2 – Part 1

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Q-1 The curved surface area of a right circular cylinder of height Equation is Equation . Find the diameter of the base of the cylinder.

A rectangle rolled into a cylinder

Curved Surface of a Cylinder Made From a Rectangle

A rectangle rolled into a cylinder

Understanding curved surface area of a cylinder.

Curved Surface Area of a Cylinder as the Area of a Rectangle

Understanding curved surface area of a cylinder.

Solution:

The radius of the base is Equation and the height Equation of the cylinder. Therefore, curved surface area of cylinder

  • Equation (Given)

  • Equation Equation

  • Equation

  • Equation

  • Equation

So, the diameter of the base is = Equation

Q-2 It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?Solution:

Total surface area of a cylinder

Total Surface Area of Cylinder

Total surface area of a cylinder

We are given that diameter of base Equation and Height Equation

Therefore, metal sheet required to make a closed cylindrical tank = Equation

  • Equation Equation

  • Equation

  • Equation

Q-3 A metal pipe is Equation long. The inner diameter of a cross section is Equation , the outer diameter being Equation (see Fig.). Find its

  1. Inner curved surface area,

  2. Outer curved surface area,

  3. Total surface area.

Ellipse c Ellipse c: Ellipse with foci A, B passing through C Ellipse c_1 Ellipse c_1: Ellipse with foci A_1, B_1 passing through C_1 Segment f Segment f: Segment [D, E] Segment g Segment g: Segment [F, G]

a Metal Pipe

A metal pipe is 77cm long, Inner diameter is4cm, outer diameter is 4.4cm

Solution:

External radius is Equation and the internal radius is Equation the length of the pipe is Equation , therefore

  • Equation

  • Equation

  • Equation

  1. Inner curved surface

    • Equation

    • Equation Equation

    • Equation

  2. Outer curved surface

    • Equation

    • Equation ( Equation )

    • Equation

  3. Total surface area of a pipe = Inner curved surface area + outer curved surface area + areas of two base

  • Equation

  • Equation ( Equation )

  • Equation

  • Equation

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