Question

The diameter and height of a cylinder are in the ratio 3:1.if the volume of the cylinder is 155232cm^3 find the total surface area of the cylinder.

Answer 1

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Answer 2

Total surface area of the cylinder is 18480 cm².

Step-by-step explanation:

Given : The diameter and height of a cylinder are in the ratio 3:1. If the volume of the cylinder is 155232 cm³.

To find : The total surface area of the cylinder ?

Solution :

Let the ratio be 'x'.

The diameter and height of a cylinder are in the ratio 3:1.

The diameter is 3x and height is x.

The radius is $r=\frac{3x}{2}$.

The volume of the cylinder is $V=\pi r^2 h$

$155232=\frac{22}{7}\times (\frac{3x}{2})^2\times x$

$155232=\frac{22}{7}\times \frac{9x^2}{4}\times x$

$x^3=\frac{155232\times 7\times 4}{22\times 9}$

$x^3=21952$

$x=\sqrt[3]{21952}$

$x=28$

The radius is $r=\frac{3\times 28}{2}=42\ cm$.

The height is $h=x=28\ cm$.

The total surface area of the cylinder is

$TSA=2\pi r^2+2\pi r h$

$TSA=2\times \frac{22}{7}\times 42^2+2\times \frac{22}{7}\times 42\times 28$

$TSA=11088+7392$

$TSA=18480$

Therefore, total surface area of the cylinder is 18480 cm².

#Learn more

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