Question

The lateral surface area of a hollow cylinder is 4224 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.


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Answer 1

$\huge\star\bf\huge\underline{ \: Given}$

$\sf\implies{The \: lateral \: surface \: \: area }$

$\sf{of \: a \: hollow \: cylinder \: is \: 4224 cm².}$

$\sf \implies{height = 33 cm}$

$\huge\star\bf\huge\underline{ \: We \: know \: that}$

$\bf {∴l= \: 2 \pi rh }\implies4224 \: {cm}^{2} = 2\pi rh$

$\bf \:\implies2\pi \: r = \frac{4224 \: {cm}^{2} }{33 \: cm} = 128 \: cm$

$\huge\star\bf\huge\underline{ \: Thus}$

$\bf{The \: length \: of \: rectangular \: sheet }$

$\bf \implies 128 \: cm$

$\huge\star\bf\huge\underline{ \: Now }$

$\bf{Perimeter \: of \: Rectangular \: sheet}$

$\bf \implies \:2 \times (length + breadth)$

$\bf \implies2 \times (128 + 33)$

$\bf \implies \: 2 \times 161 \: cm$

$\bf \implies \: 322 \: cm$

Answer 2

QUESTION:-

The lateral surface area of a hollow cylinder is 4224 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of the rectangular sheet.

WE KNOW:-

The length of rectangular sheet will be equal to the circumference of the circle. Lateral surface area of the cylinder will be equal to the area of the rectangular sheet.

GIVEN:-

Lateral surface area of a hollow cylinder = 4224 cm²

Lateral surface area of a hollow cylinder = 4224 cm²Width of rectangular sheet = 33 cm

Let length of the rectangular sheet = L

Lateral surface area of cylinder = Area of rectangular sheet

• 4224 cm² = b × L

• 4224 cm² = 33 cm × L

• L = 4224 / 33 cm = 128 cm

SO:-

The length of the rectangular sheet be 128 cm

THEREFORE:-

Perimeter of the rectangular sheet = 2 × (L + b)

• = 2 × (128 cm + 33 cm)

• = 2 × (128 cm + 33 cm)= 2 × 161 cm = 322 cm

ANSWER:-

The perimeter of the rectangular sheet is 322 cm.