Question

The ratio between the radius of the base and the height of a cylinder is 2:3 its volume is 12936m³ then JSA of the cylinder

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Answer 1

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.

$\sf\:Volume=\pi\:r^2\:h$

Now , Put the given values

$\sf\implies\:12936=\dfrac{22}{7}\times(2x)^2\times(3x)$

$\sf\implies\:12936=\dfrac{22}{7}\times(4x^2)\times(3x)$

$\sf\implies\:12936=\dfrac{22}{7}\times(12x^3)$

$\sf\implies\:x^3=\dfrac{12936\times7}{22\times12}$

$\sf\implies\:x^3=\dfrac{90522}{264}$

$\sf\implies\:x^3=343$

$\sf\implies\:x=\sqrt[3]{343}$

$\sf\implies\:x=7$

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

$\sf=2\pi\:r(r+h)$

$\sf=2\times\dfrac{22}{7}\times(14)[14+21]$

$\sf=88\times35$

$\sf=3080m^2$

Curved surface area

$\sf=2\pi\:r\:h$

$\sf=2\times\dfrac{22}{7}\times(14)\times(21)$

$\sf=88\times21$

$\sf=1848m^2$

Therefore , Total surface area of cylinder is 3080m² and curved surface area is 1848 m².

Answer 2

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