Question

A rectangular piece of psper of length 44 cm and breadth 20 cm is to be rolled along its length, to form a right circular cylinder . Find the volume of the cylinder formed.​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ There is a rectangular piece of paper which is gonna be rolled into a cylinder

• Length = 44 cm
• Breadth = 20 cm

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The Volume of the cylinder?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here as we roll the rectangular sheet then in the newly formed cylinder,

✪ Height of the cylinder will be equal to the breadth of the rectangle which is equal to 10 cm

✪ Circumference of the base of the cylinder will be equal to the length of the cylinder

━━━━━━━━━

$\underline{\bigstar\:\textsf{According to the given Question :}}$

So then we shall first find the radius of the cylinder,

➝ $\displaystyle\sf Circumference = 2\pi r$

➝ $\displaystyle\sf 44 = 2\times \dfrac{22}{7} \times r$

➝ $\displaystyle\sf \dfrac{44}{2} = \dfrac{22}{7} \times r$

➝ $\displaystyle\sf 22 = \dfrac{22}{7} \times r$

➝ $\displaystyle\sf 22\times \dfrac{7}{22} = r$

[Cancelling 22]

➝ $\displaystyle\sf \orange{Radius = 7 \ cm}$

Volume of the cylinder is given by,

$\displaystyle\underline{\boxed{\sf Volume_{Cylinder} = \pi r^2 h}}$

• r = Radius = 7 cm
• h = Height = 10 cm

Substituting the values,

➳ $\displaystyle\sf Volume_{Cylinder} = \pi r^2 h$

➳ $\displaystyle\sf \dfrac{22}{7} \times 7^2\times 10$

➳ $\displaystyle\sf \dfrac{22}{7}\times 7\times 7\times 10$

➳ $\displaystyle\sf 22\times 7\times 10$

➳ $\displaystyle\sf \pink{Volume = 1540 \ cm^3}$

$\displaystyle\sf \therefore\:\underline{\sf Volume \ of \ the \ cylinder \ is \ 1540 \ cm^3}$

$\displaystyle\sf \star\: Diagram \:\star$

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(1,6)\qbezier(5,1)(5,1)(5,6)\qbezier(1,1)(2.9,0.3)(5,1)\qbezier(1,6)(2.9,5.2)(5,6)\qbezier(1,6)(2.9,6.5)(5,6)\put(6,2.5){\vector(0,1){3.4}}\put(6.4,3){\large\sf h = 10 cm}\put(6,2.5){\vector(0,-1){1.6}}\put(2.9,6){\vector(1,0){2}}\put(2.9,6.5){\large\sf r = 7 cm}\end{picture}$

━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

       Volume = 2.31 cm³           

Step-by-step explanation:

• Height = 1.5cm

circumference of one side - 2πr = 44cm

2 × 22 / 7 × r = 4.4

r = 4.4 × 7 / 2 × 22

r = 0.7cm

• Volume of cylinder = πr²h

        = 22 / 7 × 0.7 × 0.7 × 1.5

       = 2.31 cm³