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ago in Mathematics by (16.9k points)
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Curved surface area of a hollow cylinder is 4224 cm2. A rectangular sheet having width 33 cm is formed cutting it along its height. Find perimeter of sheet.

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ago by (17.3k points)
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Best answer

Given:

Lateral surface area of hollow cylinder=4224 cm2

Height of hollow cylinder (h)=33 cm

Curved surface area of hollow cylinder =2πrh

⇒ 2πrh = 4224 cm2

⇒ 2 × \(\frac{22}{7}\) × r × 33 cm = 4224 cm2

⇒ r = \(\frac{4224\ cm^2×\ 7}{2\ ×\ 22\ ×\ 33\ cm}\)

⇒ r = \(\frac{32 \ ×\ 7}{11\ cm}\)

Since, circumference of the base of cylinder becomes length of rectangular sheet

Now Length of rectangular sheet =2πr

⇒ l = 2 × \(\frac{22}{7}\) × \(\frac{32 \ ×\ 7}{11\ }\)

⇒ l = 128 cm---(1)

Similarly, Breadth of rectangular sheet is height of cylinder.

⇒ b = 33 cm ---(2)

Perimeter of rectangular sheet =2(l+b)

= 2(128 cm+33 cm)

= 2×161 cm

= 322 cm

Therefore, the perimeter of rectangular sheet is 322 cm.

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