Question

A rectangular sheet of paper is rolled along its length to make a cylinder the sheet is 33 cm long and 32 cm wide a circular sheet paper is attached to the bottom of the cylinder find the capacity of cylinder so formed​

Answer 1

Answer

• Volume of the cylinder is 2688 cm³

Explanation

Given

• A rectangular sheer is rolled into a cylinder
• Length of the cylinder is 33 cm
• Breadth of the cylinder = 32 cm

To Find

• Volume of the cylinder

Solution

• The length of the rectangle will be the height of the cylinder and the breadth of the rectangle will be the circumference of the top and bottom
• So here we shall first find the radius and he simple substitution will give us the volume!!

✭ Radius of the cylinder

→ Circumference = 2πr

→ 32 = 2πr

→ 32/2 = πr

→ 16 = 22/7 × r

→ 16 × 7/22 = r

→ 112/22 = r

→ Radius = 56/11 cm

✭ Volume of cylinder

→ Volume = πr²h

→ Volume = 22/7 × (56/11)² × 33

→ Volume = 22/7 × 3136/121 × 33

→ Volume = {22 × 448 × 33}/121

→ Volume = 325248/121

→ Volume = 2688 cm³

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

A rectangular sheet of paper is rolled along its length to make a cylinder. The sheet is $33\:cm$ long and $32\:cm$ wide. A circular sheet paper is attached to the bottom of the cylinder find the capacity of cylinder so formed.

$\huge\bold{\mathbb{GIVEN}}$

• A rectangular sheet of paper is rolled along its length to make a cylinder.

• Length of sheet $33\:cm.$

• Width of sheet $32\:cm.$

$\huge\bold{\mathbb{DIAGRAM}}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{r}}\put(9,17.5){\sf{33\:cm}}\end{picture}$

$\huge\bold{\mathbb{SOLUTION}}$

Let's work out to find the volume!!

Let the radius of the cylinder be $r\:cm.$

Circumference of the cylinder

$\:\:\:\:\:\:\:\:\:\:=$ Width of the sheet

$\:\:\:\:\:\:\:\:\:\:=32\:cm$

We know that:

$\boxed{Circumference\:of\:cylinder=2πr\:unit}$

Let's find out the radius of the cylinder!!

$2πr=32$

$\implies 2\times{\Large{\frac{22}{7}}}\times r=32$

$\implies {\Large{\frac{(2\times22)}{7}}}\times r=32$

$\implies {\Large{\frac{44}{7}}}\times r=32$

$\implies r=32\times{\Large{\frac{7}{44}}}$

$\implies r={\Large{\frac{(32\times7)}{44}}}$

$\implies r={\Large{\frac{\cancel{224}}{\cancel{44}}}}$

$\implies r={\Large{\frac{56}{11}}}$

$\implies r=5{\Large{\frac{1}{11}}}$

So, radius $=r\:cm = 5{\Large{\frac{1}{11}}}\:cm$

$\:$

Now, we have found the radius.

We know that:

$\boxed{Volume\:of\:cylinder=πr²h\:unit³}$

Let's find out the volume of the cylinder!!

$πr²h\:unit³$

$=\{{\Large{\frac{22}{7}}}\times{\Large{(}}5{\Large{\frac{1}{11}})^{\small{2}}}\times 33\}\:cm³$

$=\{{\Large{\frac{22}{7}}}\times{\Large{\frac{56}{11}}}\times{\Large{\frac{56}{11}}}\times 33\}\:cm³$

$=\{{\Large{\frac{\cancel{22}}{\cancel{7}}}}\times{\Large{\frac{\cancel{56}}{\cancel{11}}}}\times{\Large{\frac{56}{\cancel{11}}}}\times \cancel{33}\}\:cm³$

$=(2\times 8\times 56\times3)\:cm³$

$=2688\:cm³$

$\huge\bold{\mathbb{HENCE}}$

Volume $=2688\:cm³$

$\huge\bold{\mathbb{THEREFORE}}$

The capacity of cylinder so formed is $2688\:cm³.$

$\huge\bold{\mathbb{DONE}}$