Question

The lateral surface area of a hollow cylinder is 4224 cm . It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
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Answer 1

Answer:

• LSA of a hollow cylinder = 4224 cm²
• Width of the new rectangle = 33 cm
• Perimeter = ?

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

$\displaystyle\sf :\implies LSA \ of \ Cylinder = 2\pi rh$

$\displaystyle\sf :\implies 4224 = 2\times \pi\times r\times 33$

$\displaystyle\sf {\scriptsize\qquad\bf{\because}\:\:\texttt{Breadth = Height}}$

$\displaystyle\sf :\implies 4224 = 66\pi r$

$\displaystyle\sf :\implies \dfrac{4224}{66} = \pi r$

$\displaystyle\sf :\implies 64 = \pi r$

$\displaystyle\sf :\implies\underline{\boxed{\sf r = \dfrac{64}{\pi}}}$

• The circumference of the circle will be equal to the length of the rectangular sheet

$\displaystyle\sf :\implies Length = 2\pi r$

$\displaystyle\sf :\implies Length = 2\times \pi \times \dfrac{64}{\pi}$

$\displaystyle\sf :\implies Length = 2\times 64$

$\displaystyle\sf :\implies\underline{\boxed{\sf Length = 128 \ cm}}$

$\displaystyle\underline{\textsf{Perimeter will be :}}$

$\displaystyle\sf = 2(l+b)$

$\displaystyle\sf = 2(128+33)$

$\displaystyle\sf = 2(161)$

$\displaystyle\sf \therefore\:\underline{\textsf{Perimeter will be \textbf{322 cm}}}$

Answer 2

Answer:

Perimeter will be :

\displaystyle\sf = 2(l+b)=2(l+b)

\displaystyle\sf = 2(128+33)=2(128+33)

\displaystyle\sf = 2(161)=2(161)

\displaystyle\sf \therefore\:\underline{\textsf{Perimeter will be \textbf{322 cm}}}∴

Perimeter will be 322 cm