Question

A cylindrical bucket 28 cm in diameter ;72 in height and full of water is emptied into a rectangular tank 66 cm long 28 cm wide find the height of the water level in the vessel

Answer 1

Volume of cylindrical bucket = volume of rectangular tank

π×r×r×h=l×b×h'

22×14×14×72÷7=66×28×h'

22×196×72÷7×66×28=h'

24=h'

Hence height of water level in the vessel is 24cm

Answer 2

$\underbrace{Concept\:\:Of\:\:The\:\:Question}$

In the question, diameter and height of the cylindrical bucket is given from which we will find out the radius of the cylindrical bucket and then its volume. Length and breadth of the rectangular tank is given and we have to find the height. From the question, we can say that Volume of the Cylindrical Bucket is equal to Volume of the Rectangular Tank. This helps us to find the height of the water level in the tank.

Solution :-

$\star$ Cylindrical Bucket (Measurements) :-

Diameter = 28 cm

Radius = $\frac{Diameter}{2} = \frac{28\:\:cm}{2} = 14\:\:cm$

Height = 72 cm

Volume of the Cylindrical Bucket

$=\pi \times (Radius)^{2} \times height \\ =\frac{22}{7} \times (14\:\:cm)^{2} \times 72\:\:cm \\ = \frac{22}{7} \times 196\:\:cm^{2} \times 72\:\:cm$

$\star$ Rectangular Tank (Measurements) :-

Length = 66 cm

Breadth = 28 cm

Height = ?

Volume of the Rectangular Tank

$= Length \times Breadth \times Height \\ =66\:\:cm \times 28\:\:cm \times Height$

∴ According To The Question :-

$=> Volume\:\:of\:\:the\:\:Cylindrical\:\:Bucket = Volume\:\:of\:\:the\:\:Rectangular\:\:Tank \\ \\=> \frac{22}{7} \times 196\:\:cm^{2} \times 72\:\:cm=66\:\:cm \times 28\:\:cm \times Height \\ \\ => Height = \frac{22 \times 196\:\:cm^{2} \times 72\:\:cm }{7 \times 66\:\:cm \times 28\:\:cm} \\ \\ => Height = 24\:\:cm$