NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.1 – Part 2

Q-4 The paint in a certain container is sufficient to paint an area equal to Equation . How many bricks of dimensions Equation can be painted out of this container?

Box: Rectangular Prism with surface area A=2(wh+lw+lh)

Box: Rectangular Prism

Box: Rectangular Prism with surface area A=2(wh+lw+lh)

Solution:

  • The container can paint an area Equation

  • Dimensions of brick Equation

Therefore, total surface area of a brick

  • Equation

  • Equation

  • Equation

  • Equation

Number of bricks can be painted Equation = Equation

Q-5 A cubical box has each edge Equation and another cuboidal box is Equation long, Equation wide and Equation high.

  1. Which box has the greater lateral surface area and by how much?

  2. Which box has the smaller total surface area and by how much?

Solution:

Surface area of cuboid is 2(lw+hw+lh)

Surface Area of Cuboid

Surface area of cuboid is 2(lw+hw+lh)

  • Cubical box has each edge Equation

  • Length Equation

  • Width Equation

  • Height Equation

Lateral surface area is the area of the faces along the height. That is, it is the area excluding the top and bottom. Now for cube this would be the area of any 4 faces. For the cuboid it would be Equation

Solution (i)

  • Lateral surface area of cubical box of edge Equation

  • Lateral surface area of cuboid box is Equation

  • Thus, lateral surface area of the cubical box is greater by Equation

Total surface area of cubical box of edge Equation

Total surface area of cuboidal box Equation

= Equation

= Equation

= Equation

So, total surface area of cubical box is smaller by Equation

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