Question

..
A tank 40 m long, 30 m broad and 12.5 m deep is dug in
a field 1000 m long and 30 m wide. By how much will
the level of the field rise if the earth dug out of the tank
in evenly spread over the field.

(a) 5.20 m
(b) 2 m
(c) 1.2 m
(d) 0.5 m​

Answer 1

Answer:

(d) 0.5

Step-by-step explanation:

Volume of earth taken out

=40×30×12=14400m3

Area of rectangular field

=1000×30=30000m2

Area of region of tank

=40×30=1200m2

Remaining area

=30000−1200=28800m2

Increase in height

=1440028800=0.5m

Answer 2

Answer:

Option (d) 0.5 m

Step-by-step explanation:

Given:-

• A tank 40 m long, 30 m broad and 12.5 m deep
• A tank is dug in a field 1000 m long and 30 m wide

Find:-

The level of the field rise if the earth dug out of the tank is evenly spread over the field.

Solution:-

Volume of tank = length × breadth × height

Here -

• length = 40 m
• breadth = 30 m
• height = 12.5 m

Substitute the known values above

$\implies\:\sf{40\:\times\:30\:\times\:12.5}$

$\implies\:\sf{14400\:m^3}$ ...(1)

Also,

Volume of field = length ×breadth × height

Here -

• length = 960 m = (1000 - 40)m
• breadth = 30 m

Let the height of the field be "h" m.

$\implies\:\sf{14400\:=\:960\:\times\:30\:\times\:h}$

$\implies\:\sf{14400\:=\:28800h}$

$\implies\:\sf{\dfrac{14400}{28800}\:=\:h}$

$\implies\:\sf{0.5\:=\:h}$

$\implies\:\sf{h\:=\:0.5\:m}$

OR

Area of tank = length × breadth

$\implies\:\sf{40\:\times\:30}$

$\implies\:\sf{1200\:m^2}$

Area is field = length × breadth

$\implies\:\sf{1000\:\times\:30}$

$\implies\:\sf{30000\:m^2}$

Remaining area = Area of field - Area of tank

$\implies\:\sf{(30000\:-\:1200)\:m^2}$

$\implies\:\sf{28800\:m^2}$

Now,

Volume of tank = length × breadth × height

$\implies\:\sf{40\:\times\:30\:\times\:12.5}$

$\implies\:\sf{14400\:m^3}$

$\therefore$ $\sf{height\:=\:\dfrac{Volume\:of\:tank}{Remaining\:area}}$

$\implies\:\sf{\dfrac{14400}{28800}\:=\:0.5\:m}$