Question

Find the cost of painting the outer surface of a closed box which is $ 60 $ cm long, $ 40 $ broad and $ 30 $ cm high at the rate of $ 50 $ paise per $ 20c{m^2}. $

Answer 1

Hint: We have been given the measurements of a closed box, we know that it is of the cuboidal shape. So we will first find the total surface area of the box.
The formula of total surface area of the cuboid is
  $ 2(lb + bh + hl) $ , where $ l $ is the length, $ b $ is the breadth and $ h $ is the height of the cuboid. After that we will find the cost of painting with the given data.

Complete step-by-step answer:
Let us first draw the diagram of the cuboidal box according to the question.

From the above figure we have length of the box
  $ (l) = 60cm $
The breadth of the box is
 $ (b) = 40cm $
And the height of the box
  $ (h) = 30cm $
Now the total surface area of the box is
 $ 2(lb + bh + hl) $
We will put the values in the formula and it gives:
 $ 2(60 \times 40 + 40 \times 30 + 60 \times 30)c{m^2} $
It gives us the value;
 $ 2(2400 + 1200 + 1800)c{m^2} $
By breaking the bracket and by multiplying , we have
 $ T.S.A = 2 \times 5400 = 10800c{m^2} $ .
According to the question we have been given that cost of painting $ 20c{m^2} $ is
  $ 50paise $
We will first convert the paise into rupees. We know that
 $ 100 $ paise $ = 1 $ rupee
So $ 1 $ paise can be written as
  $ \dfrac{1}{{100}} $ rupees
Therefore it gives
 $ 50paise = \dfrac{{50}}{{100}} $ rupees.
Now we have cost of $ 20c{m^2} $ is
 $ \dfrac{{50}}{{100}} $ rupees.
So we can write cost of painting $ 1c{m^2} $ is
 $ \dfrac{{50}}{{100}} \times \dfrac{1}{{20}} $ rupees.
Therefore the cost of painting of $ 10800c{m^2} $ area is
 $ \dfrac{{50}}{{100}} \times \dfrac{1}{{20}} \times 10800 $ .
It gives the cost i.e.
 $ Rs270 $ .
Hence the required total cost of painting is $ Rs270. $
So, the correct answer is “ $ Rs270. $ ”.

Note: We should note that we have used the unitary method above to find the total cost of painting the total surface area. We have been given different units in the question, so it is always best to convert the unit into the same and then solve the question, as we convert paise to rupees, and should always consider the units as well with magnitudes of each quantity. It is best to always remember the basic conversions like $ 1 $ rupee $ = 100 $ paise.