Question

Mary wants to decorate her Christmas tree. She wants to place the free on a wooden block covered with coloured paper with a picture of Santa Claus on it. 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 40 cm would she require?

Answer 1

Hint: The number of sheets required can be given by the division of the surface area of the box (cuboidal in shape) with the surface area of the sheet (square in shape).
Formula to be used:
Surface area of cuboid = 2 ( lb + bh + hl )
Surface area of square = ${a^2}$
\[number{\text{ }}of{\text{ }}sheets{\text{ (n)}} = {\text{ }}\dfrac{{surface{\text{ }}area{\text{ }}of{\text{ }}box}}{{{\text{ }}surface{\text{ }}area{\text{ }}of{\text{ sheet}}}}\]

Complete step-by-step answer:

Given:
Length of box (l) = 80 cm
Breadth of box (b) = 40 cm
Height of box (h) = 20 cm
Side of square sheet (a) = 40 cm
Now,
i) Surface area of box = 2 ( lb + bh + hl ) (As it is a cuboid)
Substituting the given values, we get:
2 [ lb + bh + hl] = 2 ( 80 X 40 + 40 X 20 + 20 X 80 )
= 2 ( 3200 + 800 + 1600 )
= 2 X 5600
= 11200
Surface area of cuboid = \[11200c{m^2}\] __________ (1)
ii) Surface area of sheet = ${a^2}$ (As it is a square)
Substituting the given value, we get:
${a^2}$ = ${\left( {40} \right)^2}$
= 1600
Surface area of sheet = \[1600c{m^2}\] __________ (2)

iii) The number of sheets (n) required for the box can be given as:
\[number{\text{ }}of{\text{ }}sheets{\text{ (n)}} = {\text{ }}\dfrac{{surface{\text{ }}area{\text{ }}of{\text{ }}box}}{{{\text{ }}surface{\text{ }}area{\text{ }}of{\text{ sheet}}}}\]


Substituting the calculated values from (1) and (2), we get:
$
  n = \dfrac{{11200}}{{1600}} \\
  n = 7 \\
 $
Therefore, she requires 7 square sheets of paper of side 40 cm to make the box of given dimensions

Note: When the two or areas are divided, their units must be the same i.e. if one is in $c{m^2}$, the other can’t be in ${m^2}$. All the sides in a square are equal but as cuboid is a 3 – D figure for a rectangle, it has different dimensions for length, breadth, and height