Question

A square plate of side $Xcm$ is $8mm$ thick. If its volume is $2880c{m^3}$, find the value of $X$?

Answer 1

Hint: In order to find the value of $X$, first convert the thickness into centi-metres as it is given in milli-metres. For that multiply the thickness with $\dfrac{1}{{10}}$. Then put the values in the formula for volume of a square plate that is $Volume = area \times thickness$.

Formula used:
$1mm = \dfrac{1}{{10}}cm$
Area of square is $Area = {\left( {side} \right)^2}$.
Volume of square plat is $Volume = area \times thickness$.

Complete step-by-step answer:
We are given that side of the plat is $Xcm$, thickness is $8mm$and its volume is $2880c{m^3}$. Since, the volume is given in centimetres so, need to convert the thickness into centimetres.
Since, we know that $1cm = 10mm$ that implies $1mm = \dfrac{1}{{10}}cm$.
So, to convert $8mm$into $cm$, multiplying the value with $\dfrac{1}{{10}}$, and we get:
$8mm = 8 \times \dfrac{1}{{10}}cm = 0.8cm$.
Since, it is a square plat so, the length and breadth would be of same size, that is $Xcm$.
From the formula for volume of the square plat, we know that it is: $Volume = area \times thickness$.
And, area of square is $Area = {\left( {side} \right)^2}$.
So, substituting the side in Area, and we get:
$Area = {\left( {side} \right)^2} = {\left( X \right)^2} = {X^2}$
Substituting the value of Area, thickness and Volume in the Volume, we get:
$2880 = {X^2} \times 0.8$
Dividing both the sides by $0.8$:
$
  \dfrac{{2880}}{{0.8}} = \dfrac{{{X^2} \times 0.8}}{{0.8}} \\
   = > {X^2} = \dfrac{{2880}}{{0.8}} = 3600 \\
 $
Applying square root both the sides:
$
  {X^2} = 3600 \\
  \sqrt {{X^2}} = \sqrt {3600} \\
 $
Since, we know that $\sqrt {{X^2}} = \sqrt {X \times X} = X$ and $\sqrt {3600} = \sqrt {60 \times 60} = 60$.
So, from this we get that:
$
  \sqrt {{X^2}} = \sqrt {3600} \\
  X = 60cm \\
 $

Therefore, the side of the square plat $X$ is $60cm$.

Note: It’s very important to have all the values in the same units, we cannot take one value in centi-metre and other in milli-metre. So, convert the inappropriate unit into the common unit which is being followed by other values, then solve further.
We can directly put the side in the formula for volume $Volume = length \times breadth \times thickness$, as length and breadth would be same for a square, that’s why we take area.