The ratio of the radius and height of cylinder 2: 3 if its volume is 12936m^3 find tsa of cylinder
Answers
Answer:
Given :
Ratio between the radius of the base and tht height of a cylinder is 2 : 3.
Volume is 12936m³
To Find
Total surface area of cylinder
and curved surface ara
Solution :
According to the Question :
Ratio between the radius of the base and tht height of a cylinder is 2 : 3.
Let the radius of cylinder be 2x and height be 3x.
\sf\:Volume=\pi\:r^2\:hVolume=πr
2
h
Now , Put the given values
\sf\implies\:12936=\dfrac{22}{7}\times(2x)^2\times(3x)⟹12936=
7
22
×(2x)
2
×(3x)
\sf\implies\:12936=\dfrac{22}{7}\times(4x^2)\times(3x)⟹12936=
7
22
×(4x
2
)×(3x)
\sf\implies\:12936=\dfrac{22}{7}\times(12x^3)⟹12936=
7
22
×(12x
3
)
\sf\implies\:x^3=\dfrac{12936\times7}{22\times12}⟹x
3
=
22×12
12936×7
\sf\implies\:x^3=\dfrac{90522}{264}⟹x
3
=
264
90522
\sf\implies\:x^3=343⟹x
3
=343
\sf\implies\:x=\sqrt[3]{343}⟹x=
3
343
\sf\implies\:x=7⟹x=7
Thus ,
Radius = 2x = 14 m
Height = 3x = 21 m
Now , We have to find Total surface area and curved surface area of cylinder.
Total surface area of cylinder
\sf=2\pi\:r(r+h)=2πr(r+h)
\sf=2\times\dfrac{22}{7}\times(14)[14+21]=2×
7
22
×(14)[14+21]
\sf=88\times35=88×35
\sf=3080m^2=3080m
2
Curved surface area
\sf=2\pi\:r\:h=2πrh
\sf=2\times\dfrac{22}{7}\times(14)\times(21)=2×
7
22
×(14)×(21)
\sf=88\times21=88×21
\sf=1848m^2=1848m
2
Therefore , Total surface area of cylinder is 3080m² and curved surface area is 1848 m².