Question

Question 3
A cistern measuring $150cm\times 120cm\times 110$ cm has $129600c{m}^3$ water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being $22.5cm\times 7.5cm\times 6.5cm?$

Answer 1

Volume of cistern $=length\times width\times depth$
$=150\times 120\times 110$
$=1980000c{m}^3$
Remaining volume of cistern= Volume of cistern – Volume of water
$=1980000–129600=1850400c{m}^3$
$\text{Volume of brick}=length\times width\times height$
$=22.5\times 7.5\times 6.5$
Since the brick absorbs one seventeenth its volume hence remaining volume will be equal to $\frac{16}{17}$ the volume of brick
Remaining volume
$=22.5\times 7.5\times 6.5\times \frac{16}{17}$
$\text{Number of bricks}=\frac{\text{Remaining volume of cistern}}{\text{Remaining volume of brick}}$
$=\frac{1850400\times 17}{22.5\times 7.5\times 6.5\times 16}$
$=\frac{31456800}{17550}=1792$