Question

the lateral surface area of a cylinder of length 14 m is 220m^2. find the volume of a cylinder​

Answer 1

Answer:

Given :

$\textsf{Length of the cylinder = Height = 14 m}$

$\sf{Lateral\:surface\:area\:of\:the\:cylinder={220}^{2}}$

To find :

$\textsf{Volume of the cylinder}$

Taken :

First find the radius to find the radius use this formula .

$\sf{ \boxed{2\pi \: rh = 220}}$

Where,

v = Volume

r = Radius

h = Height

After that to find the volume of the cylinder use this formula :

$\sf{ \boxed{v = \pi \: {r}^{2} h}}$

Solution :

Radius :

$\sf \implies \: 2 \times \dfrac{22}{7} \times r \times 14 = 220$

$\: \: \: \:$

$\sf \implies2 \times \dfrac{22}{ \cancel7} \times { \cancel{14}}^ {2} \times r = 220$

$\: \:$

$\sf \implies88 \times r = 220$

$\: \:$

$\sf \implies88 r = 220$

$\: \:$

$\sf \implies \: r = \dfrac{ \cancel{220}}{ \cancel{88}}$

$\: \:$

$\sf \implies \: r = \dfrac{5}{2}$

Volume of the cylinder -:

$v \sf \implies \dfrac{22}{7} \times{( \dfrac{5}{2} )}^{2} \times 14m$

$\: \:$

$v \sf \implies \dfrac{22}{7} \times ( \dfrac{5}{2} \times \dfrac{5}{2} ) \times 14m$

$\: \:$

$v \sf \implies \dfrac{ \cancel{22}}{ \cancel{7} } \times \dfrac{25}{ \cancel{4}} \times \cancel{ 14m}$

$\: \:$

$v \sf \implies11 \times 25$

$\: \:$

$v \sf \implies {275m}^{3}$

Answer :

So , the volume of the cylinder is 275 m³.