Question

How many bricks, each measuring $ 25\;cm \times 11.25\;cm \times 6\;cm $ , will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?
A.5600
B.6000
C.6400
D.7200

Answer 1

Hint: Volume of each brick can be calculated by using the formula of the volume of cuboid and similarly, volume of wall can also be calculated. A wall is a collection of bricks placed together closely. So the volume of the wall is equal to the sum of the volume of all the bricks used to make the wall

Complete step-by-step answer:
A cuboid is a 3D shape having six rectangular faces, eight vertices and twelve edges.
Volume of a cuboid having length L, breadth B and height H is; $ V = LBH $
We know that brick is a cuboid, volume of a brick having length 25 cm, breadth 11.25 cm and height 6 cm is;
 $ \Rightarrow {V_B} = 25 \times 11.25 \times 6 $
Wall is also a cuboid, so volume of a wall having length 8 m or 800 cm, breadth 22.5 cm and height 6 m or 600 cm is;
 $ \Rightarrow {V_W} = 800 \times 22.5 \times 600 $
Now, let the number of bricks required to make the wall be n. Therefore,
Volume of 1st brick + volume of 2nd brick…… + volume of nth brick = volume of wall
n(volume of brick) = volume of wall
 $ \Rightarrow n = \dfrac{{{V_W}}}{{{V_B}}} = \dfrac{{800 \times 22.5 \times 600}}{{25 \times 11.25 \times 6}} = 32 \times 2 \times 100 = 6400 $
Therefore the number of bricks used = 6400.
So, the correct answer is “6400”.

Note: Cube and cuboid look similar to each other but a cube has six square faces while cuboid has six rectangular faces. Although they look similar in structure, they have different properties based on their edge length, diagonal length and faces. But they also have many similar properties like both of their interior angles equal to 90 degrees.