S URFACE A REAS AND VOLUMES
Recall that a cuboid, whose length, breadth and height are all equal, is called a
cube. If each edge of the cube is a, then the surface area of this cube would be
2(a × a + a × a + a × a), i.e., 6a 2 (see Fig. 13.3), giving us
Surface Area of a Cube = 6a 2
where a is the edge of the cube.
Suppose, out of the six faces of a cuboid, we only find the area of the four faces,
leaving the bottom and top faces. In such a case, the area of these four faces is called
the lateral surface area of the cuboid. So, lateral surface area of a cuboid of
length l, breadth b and height h is equal to 2lh + 2bh or 2(l + b)h. Similarly,
lateral surface area of a cube of side a is equal to 4a2.
Keeping in view of the above, the surface area of a cuboid (or a cube) is sometimes
also referred to as the total surface area. Let us now solve some examples.
Example 1 : Mary wants to decorate her Christmas
tree. She wants to place the tree on a wooden box
covered with coloured paper with picture of Santa
Claus on it (see Fig. 13.4). She must know the exact
quantity of paper to buy for this purpose. If the box
has length, breadth and height as 80 cm, 40 cm and
20 cm respectively how many square sheets of paper
of side 40 cm would she require?
Solution : Since Mary wants to paste the paper on
the outer surface of the box; the quantity of paper
required would be equal to the surface area of the
box which is of the shape of a cuboid. The dimensions
of the box are: