CLASS-7
SURFACE AREA AND VOLUME OF CUBOID

SURFACE AREA AND VOLUME OF CUBOID -

A cuboid (also known as a rectangular prism) is a three-dimensional solid object with six rectangular faces, where opposite faces are equal. It has length (l), width (w), and height (h) as its dimensions.

1. Surface Area of a Cuboid:-

The surface area is the total area of all six rectangular faces.

                   A = 2lw + 2lh + 2wh

Where:-

  • l = length
  • w = width
  • h = height
Geometry

You are essentially summing the areas of three pairs of opposite faces:-

  • 2lw for the front and back faces,
  • 2lh for the top and bottom faces, and
  • 2wh for the left and right faces.
Geometry

Surface area of a cuboid = 2 (lb+ bh+ lh)


Example.1) If the length, breadth and height of a cuboid are 5 cm, 3 cm and 4 cm. The find its total surface area.

Ans.)

Given, Length, l = 5 cm,

      Breadth, b = 3 cm

   and Height, h = 4 cm.

As per the formula -

TSA = 2(lb+bh+lh)

TSA = 2(5 x 3 + 3 x 4 + 5 x 4)

TSA = 2(15 + 12 + 20) 

TSA = 2(47) = 94 sq.cm.


Volume Of Cuboid:-

The volume is the amount of space enclosed by the cuboid.

            V= lwh

Where:

  • l, w, and h are the dimensions of the cuboid.

This formula calculates the volume by multiplying the area of the base (length × width) by the height.

Geometry

Example.1) Find the volume of a cuboid of length 20 cm, breadth 15 cm and height 10 cm.

Ans.)

Length of the cuboid = 20 cm Breadth of the cuboid = 15 cm Height of the cuboid = 10 cm

Therefore, volume of the cuboid = length × breadth × height

= (20 × 15 × 10) cm³

= 3000 cm³           (Ans.)



Example.2) If a cuboid has dimensions:

  • Length l = 5 cm,
  • Width w = 3 cm,
  • Height h = 4 cm,

Then:

  • Surface Area:- 

      A = 2(5×3) + 2(5×4) + 2(3×4)

       = 2(15) + 2(20) + 2(12)

       = 30 + 40 + 24

       = 94 cm²


  • Volume:-

       V = 5cm × 3cm × 4cm = 60 cm³     (Ans.)