The volume of a cylinder is half of its Total surface area ( in numbers) . If the radius of its base is 7cm, find the volume.
Answers
Given:-
- Volume of the cylinder is half of its total surface area.
- Radius of base = 7 cm
To find:-
Volume of the cylinder.
Solution:-
We know,
Volume of cylinder = πr²h sq.units
Total Surface Area of cylinder = 2πr(r + h) sq.units
ATQ,
1/2 Volume of cylinder = Total surface area pf cylinder
Hence,
1/2πr²h = 2πr(r + h)
= 1/2 × 22/7 × (7)² × h = 2 × 22/7 × 7 (7 + h)
= 1 × 11/7 × 7 × 7 × h = 2 × 22 × (7 + h)
= 1 × 11 × 7 × h = 44(7 + h)
= 77h = 308 + 44h
= 77h - 44h = 308
= 33h = 308
=> h = 308/33
=> h = 9.3 cm
Now,
Volume of cylinder = πr²h cu.units
Volume = 22/7 × (7)² × 9.3
Volume = 22/7 × 7 × 7 × 9.3
Volume = 22 × 7 × 9.3
Volume = 1432.2 cm³
Therefore the volume of the cylinder is 1432.2 cm³
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Concept!!
As it is given the question that half the volume of the cylinder is equal to it's total surface area. So on equating this we get the value of h i.e., haight of the cylinder. Now as we were asked to find the volume of the cylinder we put the values of radius and height in the formula of volume of cylinder. And we get the volume of the cylinder.
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Formulas Used:-
- Volume of the cylinder = πr²h cu.units
- Total Surface Area of the cylinder = 2πr(r + h) sq.units.
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