Question

11. A rectangular sheet of paper 44 cm x 20 cm is rolled along its length to form a cylinder.
Find the curved surface area and volume of the cylinder ​

Answer 1

Given :

• Length of the rectangular sheet = 44 cm

• Breadth of the rectangular sheet = 20 cm

• It is rolled along its length to form a cylinder.

To Find :

• Curved Surface Area and Volume

Solution :

Let the rectangular sheet ABCD. It is rolled along its length(Refer to the attachment)

● Height of the Cylinder = 20 cm

Circumference of Base = Length of the sheet

$\sf \longrightarrow \: Circumference = 44 \: cm$

$\sf \longrightarrow \: 2\pi \: r = 44 \: cm$

$\sf \longrightarrow \: \dfrac{44}{7} r = 44 \: cm$

$\sf \longrightarrow r = \cancel\dfrac{44 \times 7}{44}$

$\sf \longrightarrow \red{ r = 7 \: cm}$

Let's Find Curved Surface Area now :

$\bigstar \large \boxed{ \sf \: Curved \: Surface \: Area = 2\pi \: r \: h}$

$\longrightarrow \sf \: 2 \times \dfrac{22}{7} \times 7 \times 20$

$\longrightarrow \sf \cancel\dfrac{6160}{7}$

$\longrightarrow \sf \red{C.S.A = 88 0 \: {cm}^{2} }$

Let's Find Volume now :

$\bigstar \large \boxed{ \sf \:Volume \: of \: cylinder = \pi \: {r}^{2} h }$

$\longrightarrow \sf \: \dfrac{22}{7} \times 7 \times 7 \times 20$

$\longrightarrow \sf \: \cancel\dfrac{21560}{7}$

$\longrightarrow \sf \red{Volume = 3080 \: {cm}^{3} }$

Answer 2

Given :

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

To Find :

• Curved surface area of cylinder formed.
• Volume of cylinder

Solution :

Length of the rectangle, 44 cm is rolled to form a cylinder.

In such case, the length of the rectangle is the forms the circumference of the cylinder formed.

Breadth of rectangle → 20 cm.

This breadth when the rectangle is rolled into the cylinder will become the height of the cylinder formed.

Let's first find the radius of the cylinder using the formula for circumference.

Formula :

$\large{\boxed{\sf{\purple{Circumference\:=\:2\:\pi\:r\:h}}}}$

Where,

• Circumference → 44 cm
• r → radius

Block in the data,

$\longrightarrow$ $\sf{44\:=\:2\:\pi\:r}$

$\longrightarrow$ $\sf{\cancel{\dfrac{44}{2\:\:\pi}}\:=r}$

$\longrightarrow$ $\sf{\dfrac{22}{\pi}\:=r}$

$\longrightarrow$ $\sf{22\:\times\:\dfrac{7}{22}\:=r}$

$\longrightarrow$ $\sf{\cancel{\dfrac{154}{22}\:=r}}$

$\longrightarrow$ $\sf{7\:=r}$

$\large{\boxed{\sf{\red{Radius\:of\:cylinder\:formed\:=\:7cm}}}}$

Now, let's calculate the volume of the cylinder formed.

Formula :

$\large{\boxed{\sf{\pink{Volume_{cylinder}\:=\:\pi\:r^2h}}}}$

Block in the data,

$\longrightarrow$ $\sf{Volume_{cylinder}\:=\:\dfrac{22}{\cancel{7}}\:\times\:\cancel{7}\:\times\:7\:\times\:20}$

$\longrightarrow$ $\sf{Volume_{cylinder}\:=\:22\:\times\:7\:\times\:20}$

$\longrightarrow$ $\sf{Volume_{cylinder}\:=\:154\:\times\:20}$

$\longrightarrow$ $\sf{Volume_{cylinder}\:=\:3080\:}$

$\large{\boxed{\mathtt{\purple{Volume\:of\:cylinder\:=\:3080\:cm^3}}}}$

Curved Surface Area :

We have the required quantities to find the CSA of cylinder, radius and height. So, use the formula and block in the data.

Formula :

$\large{\purple{\boxed{\mathtt{CSA_{cylinder}\:=\:2\:\pi\:r\:h}}}}$

Block the data,

$\longrightarrow$ $\sf{CSA_{cylinder}\:=\:2\:\times\:\dfrac{22}{7}\:\times\:7\:\times\:20}$

$\longrightarrow$ $\sf{CSA_{cylinder}\:=\:\dfrac{44}{\cancel{7}}\:\times\:\cancel{7}\:\times\:20}$

$\longrightarrow$ $\sf{CSA_{cylinder}\:=\:44\:\times\:20}$

$\longrightarrow$ $\sf{CSA_{cylinder}\:=\:880}$

$\large{\boxed{\tt{\red{Curved\:surface\:area\:of\:cylinder\:=\:880\:cm^2}}}}$