Question

THE CURVER SURFACE AREA OF A 10m High Cylinder
is 440m. Find the volume of a cylender

Answer 1

Answer:

Volume of the cylinder = 1540m³

Step-by-step explanation:

Given :

Height of the cylinder = 10m

Curved surface area of the cylinder = 440 m²

To find :

The volume of the cylinder

Taken :

To find the volume of the cylinder use this formula -:

$\boxed{\bf{V=\pi{r}^{2}h}}$

Where,

V = Volume of the cylinder

r = Radius

h = Height

A/Q the radius of the cylinder is not given . And to find the radius of the cylinder use this formula -:

Let the radius be x

$\boxed{\bf{CSA=2\pi rh}}$

Where,

CSA = Curved surface area

Solution :

Radius of the cylinder -:

$:\implies\bf{{440m}^{2}=2\times\dfrac{22}{7}\times x\times10m}$

$:\implies\bf{{440m}^{2}=\dfrac{2\times22\times10m}{7}\times x}$

$:\implies\bf{{440m}^{2}=\dfrac{440}{7}\times x}$

$:\implies\bf{{440m}^{2}\div\dfrac{440}{7}=x}$

$:\implies\bf{\cancel{{440m}^{2}}\times\dfrac{7}{\cancel{440}}=x}$

$:\implies\bf{7m=x}$

So , the radius of the cylinder is 7m .

Volume of the cylinder -:

$:\implies\bf{V=\dfrac{22}{7}\times{7m}^{2}\times10m}$

$:\implies\bf{V=\dfrac{22}{7}\times(7m\times7m)\times10m}$

$:\implies\bf{V=\dfrac{22}{\cancel{7}}\times\cancel{49m}\times10m}$

$:\implies\bf{V=22\times7\times10m}$

$:\implies\bf{V=1540{m}^{3}}$

So , the volume of the cylinder is 1540m³ .