Question

the size of the rectangular paper is 100 cm ×44 cm . it is rolled length wise to form a cylinder. the volume of cylinder is​

Answer 1

$\pink{\bold{\underline{\underline{Question:-}}}}$ we have to Find volume of cylinder ?

$\bold{Given}\begin{cases}\sf{</strong><strong>length</strong><strong>=</strong><strong>100c</strong><strong>m</strong><strong>}</strong><strong>\</strong><strong>\</strong><strong>\sf{</strong><strong>breadth</strong><strong>=</strong><strong>4</strong><strong>4</strong><strong>c</strong><strong>m</strong><strong>}</strong><strong>\</strong><strong>\</strong><strong>\sf{</strong><strong>it\</strong><strong>:</strong><strong>is\</strong><strong>:</strong><strong>rolled\</strong><strong>:</strong><strong>length\</strong><strong>:</strong><strong>wise</strong><strong>}\end{cases}$

$\huge\boxed{\fcolorbox{fuchsia}{grey}{Solution:--}}$

$\textbf{</strong><strong>Since\</strong><strong>:</strong><strong>it\</strong><strong>:</strong><strong>is\</strong><strong>:</strong><strong>rolled\</strong><strong>:</strong><strong>length\</strong><strong>:</strong><strong>wise</strong><strong>,</strong><strong>,</strong><strong>}$

→$\textbf{</strong><strong>Its</strong><strong>\:</strong><strong>length</strong><strong>\:</strong><strong>will</strong><strong>\:</strong><strong>be</strong><strong>\:</strong><strong>length</strong><strong>\:</strong><strong>of\</strong><strong>:</strong><strong>cylinder\</strong><strong>:</strong><strong>formed</strong><strong>}$

→$\textbf{</strong><strong>Its\:</strong><strong>breadth</strong><strong>\:will\:be\:</strong><strong>cicrumference</strong><strong>\:of\:</strong><strong>base</strong><strong>\:</strong><strong>of\</strong><strong>:</strong><strong>cylinder</strong><strong>}$

$\orange{\bold{we\:know\:that}}$

Base of cylinder is in shape of circle ,

And circumference of circle is ==$\large\red{\boxed{\sf </strong><strong>2\pi \times r</strong><strong>}}$

So,

$2\pi \times r \: = 44 \\ \\ \implies \: r = \frac{\cancel44 \times 7}{ \cancel2 \times \cancel22} = 7cm$

And Height of cylinder we have = 100cm

So,

Volume of cylinder = $\large\</strong><strong>p</strong><strong>i</strong><strong>n</strong><strong>k</strong><strong>{\boxed{\sf </strong><strong>\pi \times {r}^{2} \times h</strong><strong>}}$

$v = \pi \times {r}^{2} \times h \\ \\ v = \frac{22}{7} \times {7}^{2} \times 100 \\ \\ v = 2200 \times 7 \\ \\ v = 15400cm^{3}$

$\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{\bold{</strong><strong>So\</strong><strong>:</strong><strong>Volume\</strong><strong>:</strong><strong>of\</strong><strong>:</strong><strong>cylinder\</strong><strong>:</strong><strong>Formed\</strong><strong>:</strong><strong>is</strong><strong>}}$

$\bold{\boxed{\huge{\boxed{\orange{\small{\boxed{\huge{\red{\bold{\:</strong><strong>15400cm^{3}</strong><strong>}}}}}}}}}}$

Answer 2

ANSWER:-

Given:

The size of the rectangular paper is 100cm × 44cm.

It is rolled length wise to form a cylinder.

To find:

The volume of cylinder.

Explanation:

We have,

• The size of rectangular paper is 100cm × 44cm

We know that area of rectangle: [Length × Breadth]

Therefore,

• Length of the rectangular paper= 100cm
• Breadth of the rectangular paper= 44cm

It is rolled length wise to form  cylinder:

∴ Height of cylinder, h= 100cm

& Base of cylinder= 44cm

We know that circumference of the circle: 2πr

⇒ 2× 22/7 × r = 44

⇒ 44/7 × r= 44

⇒ $r= \frac{44*7}{44} \\\\r= 7cm$

• Radius= 7cm

Now,

Formula of volume of the cylinder: πr²h cubic units

⇒ 22/7 × 7× 7× 100

⇒ (22× 7× 100)cm³

⇒ 15400cm³.

Thus,

The volume of cylinder is 15400cm³ .