Question

the length of rectangular sheet of paper is 33.It is rolled along the length into cylinder, so that it's width becomes the height of the cylinder.The volume of the cylinder is 1386cm^3. Find the width of the rectangular sheet.​

Answer 1

Answer:

refer to the attachment

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\pink{Given\::}}}}}$

The length of rectangular sheet of paper is 33.It is rolled along the length into cylinder, so that it's width becomes the height of the cylinder. The volume of the cylinder is 1386cm³.

$\bold{\Large{\underline{\rm{\red{To\:find\::}}}}}$

The width of the rectangular sheet.

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$\bold{We\:have}\begin{cases}\sf{The\:length\:of\:rectangular\:sheet\:of\:of\:paper=33}\\ \sf{The\:volume\:of\:the\:cylinder=1386cm^{3} }\end{cases}$

Let the width of the rectangle = height of the cylinder = h cm

We know that formula of the circumference of circle: 2πr

Now,

→ Circumference of the base of cylinder = 33cm

→ 2πr = 33

→ $\bold{2*\frac{22}{7} *r=33}$

→ $\bold{r=\frac{\cancel{33}*7}{\cancel{44}} }$

→ $\bold{\frac{21}{4} cm}$

&

We know that formula of the volume of cylinder: πr²h  [cubic units]

→ πr²h = 1386cm³

→ $\bold{\frac{22}{7} *\frac{21}{4} *\frac{21}{4} *h=1386}$

→ $\bold{\frac{22}{7} *{\frac{21}{4} *\frac{21}{4} *h=1386}}$

→ $\bold{22*\frac{3}{4} *\frac{21}{4} *h=1386}$

→ $\bold{h=\frac{1386*4*4}{22*3*21} }$

→ $\bold{h\:=\:\cancel{\frac{22176}{1386} }}$

→ h = 16cm

Thus,

The width of the rectangular sheet is 16cm.