Choose the correct answer from the given four options: A mason co… - Vidyadip

MCQ

Choose the correct answer from the given four options:
A mason constructs a wall of dimensions $270\ cm \times 300\ cm \times 350\ cm$ with the bricks each of size $22.5\ cm \times 11.25\ cm \times 8.75\ cm$ and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is:

A
$11100$
✓
$11200$
C
$11000$
D
$11300$

✓

Answer

Correct option: B.

$11200$

Volume of the wall $=270 \times 300 \times 350=28350000 \ cm^3$
$[\because$ volume of chboid $=$ lenth $\times $ breadth $\times $ height$]$
Since, $\frac{1}{8}$ space of wall is covered by mortar.
So, remainig space of wall $=$ Volume of wall $-$ Volume of mortar
$=28350000-28350000\times\frac{1}{8}$
$=28350000-3543750=24806250\text{cm}^3$
Now, volume of one birck $= 22.5 \times 1125 \times 875 = 2214.844\ cm^3$
$[\because$ volume of chboid $=$ lenth $\times $ breadth $\times $ height$]$
$\therefore$ Required number of bricks $=\frac{24806250}{2214.844}=11200\ (\text{approx})$
Hence, the number of used to construct the wall is $11200.$

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