Question

C.s.a of a cylinder is 4400 cm square and the circumference of it's base is 110 cm . Find the height and volume of a cylinder.

Answer 1

Step-by-step explanation

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

C.S.A of a cylinder is 4400 cm² and the circumference of it's base is 110 cm.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The height of cylinder and their volume.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We know that formula of the perimeter of circle :

$\boxed{\bf{Circumference=2\pi r}}}}}$

$\longrightarrow\sf{2\pi r=110}\\\\\longrightarrow\sf{2\times \dfrac{22}{7} \times r=110}\\\\\\\longrightarrow\sf{\dfrac{44}{7} \times r=110}\\\\\\\longrightarrow\sf{r=\dfrac{\cancel{110} \times 7}{\cancel{44}} }\\\\\\\longrightarrow\sf{r=(2.5\times 7)cm}\\\\\\\longrightarrow\sf{\green{r=17.5\:cm}}$

We know that formula of the curved surface area of cylinder :

$\boxed{\bf{C.S.A=2\pi rh }}}}}$

$\longrightarrow\sf{2\pi rh=4400}\\\\\\\longrightarrow\sf{2\times \dfrac{22}{7} \times 17.5\times h=4400}\\\\\\\longrightarrow\sf{\dfrac{44}{7} \times 17.5\times h=4400}\\\\\\\longrightarrow\sf{\cancel{\dfrac{770}{7}} \times h=4400}\\\\\\\longrightarrow\sf{110\times h=4400}\\\\\\\longrightarrow\sf{h=\cancel{\dfrac{4400}{110} }}\\\\\\\longrightarrow\sf{\green{h=40\:cm}}$

We know that formula of the Volume of cylinder :

$\boxed{\bf{Volume=\pi r^{2} h\:\:\:\:\:(cubic\:unit) }}}}}$

$\longrightarrow\sf{Volume=\dfrac{22}{7} \times (17.5)^{2} \times 40}\\\\\\\longrightarrow\sf{Volume=\dfrac{22}{\cancel{7}} \times \cancel{306.25} \times 40}\\\\\\\longrightarrow\sf{Volume=(22\times 43.75\times 40)cm^{3} }\\\\\\\longrightarrow\sf{Volume=(22\times 1750)cm^{3} }\\\\\\\longrightarrow\sf{\green{Volume=38500\:cm^{3}}}$

Thus;

The volume of the cylinder is 38500 cm³ and height is 40 cm .