Question

Johny wants to stitch a cover for his C.P.U whose length, breadth and height are \[20cm\] , \[45cm\] and \[h = 50cm\] respectively. Find the amount he has to pay if it costs \[Rs\] \[50\] per \[sq.m\] .

Answer 1

Hint: We know that the cuboidal box has six sides, but one side is open, Hence the total surface area of the cuboidal box when one side is open is the difference between the surface area of the cuboidal box and the area of the open side.

Complete step by step solution:
Since the cover is in the shape of a one face open cuboidal box (3-dimensional box).
Suppose \[l\] is the length of the box, \[b\] be the breadth of the box and \[h\] be the height of the box. Then given length \[l = 25cm\] , breadth \[b = 45cm\] and height \[h = 50cm\] .
 Since we know that \[1m = 100cm\]
  \[ \Rightarrow 1\; cm = \dfrac{1}{{100}}\;m\] .
Then \[l = 0.25m\] , \[b = 0.45m\] and \[h = 0.5\;m\] .
Hence the total surface area of the cuboidal box when one side is open is the difference between the surface area of the cuboidal box and the area of the open side.
 \[
   \Rightarrow 2(lb + bh + hl) - lb \\
   \Rightarrow 2(bh + hl) + lb \\
   \Rightarrow 2(0.45 \times 0.5 + 0.5 \times 0.2) + 0.2 \times 0.45 \\
   \Rightarrow 0.74\;sq.m \;
\]
Since the given cost of \[1\;sq.m\] is \[Rs\] 50.
Hence, the cost of \[0.74\;sq.m\] of cloth is \[50 \times 0.74\; = Rs\;37\] .
So, the correct answer is “RS 37”.

Note: Note that converting centimeter to meter is important. If sides of the cuboidal box are equal then the cuboidal box is known as the cube. In other words if length \[ = \] breadth \[ = \] height in the cuboidal box then it is known as the cube.