Question

A box is in the form of a cuboid whose external measures are 50 cm x 40 cm x 25 cm. Then base, the side faces, and back face are to be painted black. Find the area to be painted.

Answer 1

Hint: In the above question, we will find the area of the base, side faces, and back face. We will use the surface areas of each side in the cuboid to get the required answer.

Complete step by step solution:
Given,
Length $= 50 cm$
Breadth $= 40 cm$
Height $= 25 cm$

Also given that the base, the side faces, and the back face are to be painted.
$\text{Area to be painted black = (Area of the base) + 2(Area of the side faces) + (Area of the back face)}$
$=(length \times breadth) + 2(breadth \times height) + (length \times height)$
\[ = (50 \times 40) + 2(25 \times 40) + (50 \times 25)\] (Putting the value of Length, breadth and height)
$ = 5250c{m^2}$.

$\therefore$ The Area to be painted black is 5250$c{m^2}$.

Note:
In these types of questions, while calculating the perimeter of a semicircle we need to keep a few things in our mind precisely. If you think that half of the perimeter of a circle is the perimeter of a semicircle then you are wrong. If you look at the semicircle then you will notice that its perimeter must include the round portion and the diameter of a semicircle.