the curved surface area of cylinder pillar is 264 metre square and its volume is 924 cm cube find the diameter and the height of pillar...
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Answers
Question : -
The curved surface area of a cylindrical pillar is 264 m² and it's volume is 924 m³. Find the diameter and height of pillar ?
ANSWER
Given : -
The curved surface area of a cylindrical pillar is 264 m² and it's volume is 924 m³.
Required to find : -
- Diameter of the cylinder ?
- Height of the cylinder ?
Formula used : -
CSA of a cylinder is 2πrh
Volume of a cylinder is πr²h
Solution : -
The curved surface area of a cylindrical pillar is 264 m² and it's volume is 924 m³.
So,
We know that;
CSA of a cylinder = 2πrh
Volume of a cylinder = πr²h
This implies;
2πrh = 264 ...... (1)
Consider this as Equation-1
Similarly,
πr²h = 924 ...... (2)
Consider this as Equation-2
Now,
According to problem;
Divide Equation-2 by Equation-1
(πr²h)/(2πrh) = (924)/(264)
[ Like terms will be cancelled in both numerator and denominator ]
(r)/(2) = (924)/(264)
r = (924)/(264) x 2
r = 3.5 x 2
r = 7 meters
Hence,
- Radius of the cylinder = 7 meters
Now,
Let's find the diameter of the cylinder
Since, we know that
Diameter = 2 x radius
Diameter of the cylinder = 2 x 7
- Diameter of the cylinder = 14 meters
Now,
Let's find the height of the cylinder !
We know that;
CSA of the cylinder is 264 m²
This implies;
2πrh = 264
2 x (22)/(7) x 7 x h = 264
44 x h = 264
h = (264)/(44)
h = 6 meters
- Height of the cylinder = 6 meters
Question is solved !
Answer:
Curved surface area of cylinder = 264 m²
volume of cylinder = 924 m³
We know that
CSA of cylinder = 2πrh
264 = 2*22/7*r*h
r*h = (264*7)/44
r*h = 1848/44
r*h = 42
h = 42/r ……(1)
Now,
volume of cylinder = πr²h
Substituting the value of h = 42/r in the volume equation, we get
924 = 22/7*r²*42/r
924r = 924*7
r = 7 m
So, Radius is 7 m and the diameter will be 7*2 = 14 m.
And the height of the cylinder =h = 42/r= 42/7 = 6 m