Question

A square brass plate of side $x$ cm is 1 mm thick and weighs 5.44 kg. If 1 $c{{m}^{3}}$ weighs 8.5 grams. Find the value of $x$ ?

Answer 1

Hint: A square brass plate has the same length and breadth, l=b. We are given the height of the square plate in the question. And we are also given the total weight of it. The key point here is that the question also provided us with the weight of 1 $c{{m}^{3}}$ of brass. So now, we have to find out how much volume of brass makes up to 5.44 kg. This is simple cross multiplication.

Complete step-by-step solution:
A square plate has the same length and breadth. Let us consider length = breadth = l.
Now let us find the volume of the square brass plate.
Let us convert the 5.44 kg to grams. So 5.44$\times $1000 = 5440 grams.
If 1 $c{{m}^{3}}$ of brass plate weighs 8.5 grams, what will be the volume of 5440grams?
It would be $\dfrac{5440grams\times 1c{{m}^{3}}}{8.5grams}$ .
Upon simplification we get that the volume of 5440 grams of brass plate would be 640 $c{{m}^{3}}$ .
Generally , we know that volume = area $\times $ height.
We already know the height of a square brass plate. It is 1 mm.
Let us convert this 1 mm into cm . We know that 1 cm = 10 mm.
So 1 mm = 0.1 cm. So the height of the square brass plate is 0.1 cm.
We already mentioned that length and breadth of a square is the same.
Volume = l$\times $ l$\times $ 0.1 cm
640 $c{{m}^{3}}={{l}^{2}}\times $ 0.1 cm.
Dividing both sides with 0.1 cm , we get the following :
6400 = ${{l}^{2}}$
Let us take square roots on both sides.
$\begin{align}
  & l=\sqrt{6400} \\
 & l=80 \\
\end{align}$
So we got the length of one side to be 80 cm.
$\therefore $ The side of a square brass plate which weighs 5.44 grams is 80 cm.

Note: We have to be very careful while solving these kinds of mensuration questions. There is a lot of scope for calculation errors. We should be very careful with the units. Always keep the entire sum in only one unit of measurement so there won’t be any kind of confusion at the end. We should also remember all the basic formulae of mensuration.