Question

A rectangular sheet of paper, 44cm*20cm is rolled along its length to form a cylinder. Find the volume of the cylinder

Answer 1

Solution :

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

A rectangular sheet of paper, 44cm × 20 cm is rolled along its length to form a cylinder.

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

The volume of the cylinder.

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

We know that formula of the volume of cylinder;

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

We have rectangular sheet :

• Length = 44 cm

• Breadth = 20 cm

Since the we know that the length of the rectangular sheet equal to the circumference.

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

$\longrightarrow\sf{2\pi r=44}\\\\\longrightarrow\sf{2\times \dfrac{22}{7} \times r=44}\\\\\longrightarrow\sf{\dfrac{\cancel{44}}{7} \times r=\cancel{44}}\\\\\longrightarrow\sf{r=\dfrac{44\times 7}{44}} \\\\\longrightarrow\sf{\orange{r=7\:cm}}$

Now;

• Radius = 7 cm
• Height = 20 cm

$\longrightarrow\sf{Volume\:_{cylinder}=\pi r^{2} h}\\\\\\\longrightarrow\sf{Volume\:_{cylinder}=\dfrac{22}{\cancel{7}} \times \cancel{7}\times 7\times 20}\\\\\\\longrightarrow\sf{Volume\:_{cylinder}=(22\times 7\times 20)\:cm^{3} }\\\\\\\longrightarrow\sf{\orange{Volume\:_{cylinder}=3080\:cm^{3} }}$

Thus;

The volume of cylinder is 3080 cm³ .

Answer 2

Answer:

Step-by-step explanation:

length of the rectangular sheet l=44cm

breadth of the rectangular sheet b =20cm

then, the radius r of the cylinder=circumference of the base of cylinder =2pir

44=2x22/7r

44x7/44

r=7

height h of the cylinder =20cm

volume of cylinder =pi^2h

V=22/7x7x7x20

V=22x7x20

V=3080cm^3

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