a rectangular vessel of dimension 20 cm, 15 cm, 11 cm is full of water. if the water is poured into an empty cylindrical vessel of radius 10 cm find height of water in cylindrical tank
Answers
Answer:
10.5 cm
Step-by-step explanation:
The height of water present in the cylindrical vessel is 10.5cm.
Step-by-step explanation:
Given:-
A rectangular vessel of dimension 20 cm, 15 cm, 11 cm is full of water. if the water is poured into an empty cylindrical vessel of radius 10 cm .
To find:-
Find height of water in cylindrical tank?
Solution:-
The dimensions of a rectangular vessel are 20cm
,15 cm and 11 cm
Let the length be 20 cm
Let the breadth be 15 cm
Let the height be 11 cm
we have ,
l= 20 cm
b= 15 cm
h = 11 cm
Total capacity of the tank filled by water
=>Volume of the cuboid
=>lbh cubic units
=>Volume = 20×15×11 cubic cm
=>Volume = 3300 cubic cm
Volume of the rectangular vessel = 3300 cm^3
The same quantity of water poured in the cylindrical vessel then
Radius of the cylindrical vessel (r) = 10 cm
Let the height of the vessel be h cm
Capacity of the cylindrical vessel
=>Volume of the cylinder
=>πr^2 h cubic units
=>(22/7)×(10)^2 ×h cubic cm
=>Volume = (22×10×10×h)/7 cm^3
Volume of cylindrical vessel = 2200h/7 cm^3
According to the given problem
Volume of the rectangular vessel = Volume of the cylindrical vessel
=>3300 = 2200h/7
=>3300×7 = 2200h
=>2200h = 3300×7
=>2200h = 23100
=>h = 23100/2200
=>h = 231/22
=>h= 21/2
=>h = 10.5 cm
Height = 10.5 cm
Answer:-
Height of water in cylindrical tank = 10.5 cm
Used formulae:-
- Volume of a cuboid = lbh cubic units
Where, l= length,b=breadth ,h=height
- Volume of a cylinder = πr^2h cubic units
Where, r = radius , h=height and π=22/7