Question

a cylindrical tank has a lateral surface area of 504.4 m^2 and height of 14 cm. Find the base area and the volume ?

Answer 1

Given :

Height = 14cm

Lateral surface area = 504.4${m}^{2}$

Base area = 2$\pi$r

We know that,

$\boxed{\bold{Lateral\:surface\:area = 2\pi rh}}$

According to the question,

$\implies\bold{Lateral\:surface\:area = 5044000{cm}^{2}}$

$\implies\bold{2\pi r =\dfrac{5044000}{14}cm}$

$\implies\bold{2\pi r = 360285.71 cm}$

$\therefore{\bold{Base\:Area=360285.71cm}}$

Now , we have to find the volume.

To find volume we need to find radius firstly .

$\implies\bold{2\pi r= 360285.71cm}$

$\implies\bold{r = \dfrac{360285.71cm}{2\pi}}$

$\implies\bold{r= \dfrac{36028571cm\times 7}{44\times 100}}$

$\implies\bold{r=57318.18cm}$

$\therefore{\bold{Radius=57318.18cm}}$

We know that,

$\boxed{\bold{volume=\pi{r}^{2}h}}$

$\implies\bold{volume=1.44556\times {10}^{11}= 144556000000{cm}^{3}}$