Question

Find the cost of painting a wooden box which is in the shape of a cube of side \[11cm\] at the \[50\] paisa per square centimetre.

Answer 1

Hint: To find the total cost, firstly we will calculate the area of the given figure and then multiply it with the per unit cost.

Formula used: Area of a square $ = {(side)^2}$, Total cost $ = Total{\text{ a}}rea \times \cos t{\text{ per unit}}$


Complete step by step solution:
1. Wooden box is in the shape of a cube. A Cube is a three dimensional figure having all sides equal which implies that in cube, length, breadth and height are equal and we can say it as side of a cube.

2. Also, the cube has six equal surfaces of a square shape. Each square has a side equal to the side of a cube.
3. To find the total painting area of the cube.
We need to calculate area of one square face then multiply it by \[6\]as wooden cubical box has \[6\]surfaces in the shape of
a square.
4. Now first we calculate the area of one square face.
We know that area of the square $ = {(side)^2}$, where the side of the square is given as \[11cm\].
Therefore, area of the square face $ = {\left( {11} \right)^2}$
Area of square face $ = 121c{m^2}$
5. Area of the cubical wooden box = 6 Area of one square surface
$ = 6 \times 121$
$ = 726c{m^2}$
6. To find the total cost of painting a wooden box. We multiply the area of the wooden box with per unit cost.
$ Total{\text{ cost}} = Area{\text{ }}of{\text{ }}wooden{\text{ }}box \times \operatorname{Cos} t{\text{ }}per{\text{ }}unit{\text{ }}area$
$
  Total{\text{ cost}} = 726 \times \dfrac{{50}}{{100}} \\
  Total{\text{ cost}} = 726 \times \dfrac{5}{{10}} \\
  Total{\text{ cost}} = 726 \times \dfrac{1}{2} \\
 $
$ Total{\text{ cost}} = 363$
7. Therefore, total cost of painting a wooden box is Rs.\[363\]


Note: Total cost of painting any figure always depends upon two factors i.e. area of the figure and per unit cost of painting.After finding out the area , make sure to find out the cost too,do not leave the answer after finding out the area