Question

How many paint tins having spread capacity of $100{\text{c}}{{\text{m}}^2}$ will be required to paint external surface of box having dimension $80{\text{cm}} \times 50{\text{cm}} \times 25{\text{cm}}$

Answer 1

Hint: The external surface of the box looks like a cuboid. First, we have to find the area of the cuboid. The spread capacity of the paint tin is given. By dividing the area and the capacity of one tin we can get the number of tins required to paint the external surface of the box.

Formula used: The formula used for this question is,
The surface area of the box is,
 $\text { Area of Box} = 2({\text{lb + bh + lh)}}$
where,
 ${\text{l}}$ be the length of the box
 ${\text{b}}$ be the breadth of the box
 ${\text{h}}$ be the height of the box
The number of paint tins N, $ = \dfrac{{{\text{area of external surface of box}}}}{{{\text{capacity of one paint tins}}}}$

Complete step-by-step answer:
The data given in the question,
The spread capacity of one paint tin is $100{\text{c}}{{\text{m}}^2}$ .
The length of box, ${\text{l}} = 80{\text{cm}}$
The breadth of box, ${\text{b}} = 50{\text{cm}}$
The height of box, ${\text{h}} = 25{\text{cm}}$

Substitute the length, breadth and height in the area formula,
 $ \Rightarrow {\text{Area}}\,{\text{of}}\,{\text{box}} = 2[(80)(50){\text{ + (50)(25) + (25)(80)]}}$
Simplifying the above we get,
 $ \Rightarrow {\text{Area}}\,{\text{of}}\,{\text{box}} = 2[4000{\text{ + 1250 + 2000]}}$
By adding the values in the bracket we get,
 $ \Rightarrow {\text{Area}}\,{\text{of}}\,{\text{box}} = 2 \times 7250$
By multiplying we get,
 $ \Rightarrow {\text{Area}}\,{\text{of}}\,{\text{box}} = 14500{\text{c}}{{\text{m}}^2}$
Substitute the area of box value and capacity of one tin in the number of paint tin formula,
 $ \Rightarrow {\text{the required number of paint tins}} = \dfrac{{14500}}{{100}}$
By solving the above we get,
 $ \Rightarrow {\text{the required number of paint tins}} = 145$
 $\therefore $ The required number of paint tins to paint the external surface of box $ = 145$ tins.
Hence, $145$ paint tins are required to paint the external surface of box having dimension $80{\text{cm}} \times 50{\text{cm}} \times 25{\text{cm}}$

Note: The cuboid has six rectangular faces. So to find the surface area of the cuboid we have to add all the six faces of the rectangle. The width of the cuboid is the line directly proportional with the length.