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Question 5

The length of a rectangular sheet of paper is 33 cm. It is rolled along its length into a cylinder so that width becomes height of the cylinder. The volume is 1386 cubic cms. The width of the rectangular sheet (in cm) is

Rolling along the length turns the length into the base circumference, so $$2\pi r = 33$$, giving $$r = \frac{33 \times 7}{2 \times 22} = 5.25$$ cm. From $$\pi r^2 h = 1386$$, we get $$h = \frac{1386}{86.625} = 16$$ cm, which is the width of the sheet.

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