Surface Area of a Cuboid = $2(lb + bh + hl)$.
where $l$ = length , $b$ = breadth and $h$ = height of cubiod.
In a cube , l=b=h , hence surface are of cube = $2(l×l + l×l + l×l)$
= $6l^2$
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
Similarly,lateral surface area of a cube of side $a$ is equal to $4a^2$.
lateral surface area of a cube of side = $4a^2$
EXERCISE 13.1
1. A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened at the
top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1 $m^2$ costs ₹ 20.
2. The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the
cost of white washing the walls of the room and the ceiling at the rate of
₹ 7.50 per $m^2$.
3. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four
walls at the rate of ₹ 10 per $m^2$ is ₹15000, find the height of the hall.
[Hint : Area of the four walls = Lateral surface area.]
4. The paint in a certain container is sufficient to paint an area equal to 9.375 $m^2$. How many bricks of dimensions 22.5 $cm$ × 10 $cm$ × 7.5 $cm$ can be painted out of this
container?
5. A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm
wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
6. A small indoor greenhouse (herbarium) is made entirely of glass panes (including
base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.
(i) What is the area of the glass?
(ii) How much of tape is needed for all the 12 edges?
7. Shanti Sweets Stall was placing an order for making cardboard boxes for packing
their sweets. Two sizes of boxes were required. The bigger of dimensions
25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the
overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is
₹ 4 for 1000 $cm^2$, find the cost of cardboard required for supplying 250 boxes of each
kind.
8. Parveen wanted to make a temporary shelter for her car, by making a box-like structure
with tarpaulin that covers all the four sides and the top of the car (with the front face
as a flap which can be rolled up). Assuming that the stitching margins are very small,
and therefore negligible, how much tarpaulin would be required to make the shelter of
height 2.5 m, with base dimensions 4 m × 3 m?