Question

A rectangular water tank can contain 210 litres of water. If the length and breadth of the tank are 50 cm and
60 cm, find the height of the tank.​

Answer 1

★ Given:

A rectangular water tank can contain 210 litres of water.

Length of the tank = 50 cm

Breadth of the tank = 60 cm

★ To find:

The height of the tank.

★ Solution:

$\sf{\boxed{Litres\:to\:cm^3=multiply\:by\:1000}}$

So, 210 litres = 210 x 1000 cm³

= 210000 cm³

Volume of a cuboid = lbh ----- (1)

Given volume = 210000 cm³ ----- (2)

Combining equations (1) and (2)

lbh = 210000 cm³

Length = 50 cm

Breadth = 60 cm

Height = ?

Substituting the values in the equation:

50 x 60 x h = 210000 cm³

3000h = 210000 cm³

h = 210000/3000

h = 70 cm

Hence the required height of the tank is 70 cm.

Important Volume Formulae:

→ Volume of cuboid = lbh

→ Volume of cube = a³

→ Volume of cylinder = πr²h

→ Volume of cone = 1/3πr²h

→ Volume of sphere = 4 /3πr³

Answer 2

Given :

1. A rectangular water tank contain 210 litres of water.
2. Length and breadth of the tank are 50cm and 60cm.

Observation :

• Shape = cuboid
• Length = 50cm
• Breadth = 60cm
• Volume = 210 litres

To Find :

• Height of the tank

Formula Applied :

$\sf{\textsf{Volume}_{\textsf{(cuboid)}}}= \sf{lbh\: cu.units}$

• l = length
• b = breadth
• h = height

Solution :

• The height of the tank can be obtained using the formula of capacity of tank

• To substitute the values in the formula we have to convert the volume of tank from litres to cubic units. So let's convert the volume of water from litres to $cm^3$

${\underline{\boxed{\sf{1 \:litre = 1000\:cm^3 }}}}$

$\rightarrow \sf {210\:litres = 210 \times 1000 cm^3}$

${\underline{\boxed{\sf{Volume \: of\:tank = 210000\:cm^3}}}}$

• So now let's substitute the values in formula to obtain height of the tank.

$\rightarrow \sf{Volume\:of\:tank=lbh\:cu.units}$

$\rightarrow \sf{210000\:cm^3 = 50 \times 60 \times h}$

$\rightarrow \sf{210000\:cm^3} = 3000 \times h$

$\rightarrow \sf{\frac{210000}{3000} = h}$

${\underline{\boxed{\sf{height\:of\:tank = 70cm}}}}$