Question

A brick has a cubic shape and has an edge of length 45 cm. How many such bricks can fit in a room having a length of 4.5 m, breadth of 2.7 m, and height of 1.8 m.

Answer 1

Hint: At first find the volume of cube using formula volume equals to \[{{\left( \text{edge} \right)}^{3}}\] and then find the volume of cuboid using formula length \[\times \] breadth \[\times \] height. Then divide the volume of the cuboid with that of the cube. Also make sure calculations should be done either in ‘cm’ or ‘m’.

Complete step-by-step answer:
In the question a brick has a cuboid shape and has an edge of 45 cm. Now, we have to find a number of bricks that can fit in a room having a length of 4.5 m, breadth of 2.7 m and height of 1.8 m.
Now, we know that the dimension of the room given is in meters so the edge of the cube should also be changed to a meter.
Edge of the cube is 45 cm which we can rewrite as 0.45 m.
Now, as we know the edge of the cube so we can also find volume of cube using formula,
\[\text{volume}\ \text{=}\ {{\left( \text{edge} \right)}^{3}}\]
So, \[\text{volume}\ \text{=}\ {{\left( 0.45 \right)}^{3}}\ =\ 0.091125\]
Hence the volume of cuboid brick is 0.091125.
Now as we know that room’s shape is of cuboid and we can find its volume using formula,
\[\text{volume}\ \text{=}\ \left( length \right)\times \left( breadth \right)\times \left( height \right)\]
Here, the length is 4.5 m, breadth is 2.7 m and height is 1.8 m.
So, \[\text{volume}\ \text{=}\ 4.5\times 2.7\times 1.8\ =\ 21.87\ {{m}^{3}}\]
Now let’s take that n number of bricks fits in the room, so we can say that,
\[\text{n}\times \left( \text{volume of 1 brick} \right)\ \text{=}\ \left( \text{volume of room} \right)\]
\[\text{n}\times 0.091125\ \text{=}\ 21.87\]
So, \[\text{n}\ \text{=}\ \dfrac{21.87}{0.091125}\ =\ 240\]
Hence, the volume of n is 240.
Hence, the total number of bricks is 240.

Note: Students generally don’t read the question properly and make mistakes by taking the measurement of the edge of the cube in cm instead of changing to meter.