A rectangular sheet of metal $11$ cm $\times 4$ cm is rolled along its length to form a cylinder (so its…

A rectangular sheet of metal $11$ cm $\times 4$ cm is rolled along its length to form a cylinder (so its length becomes the circumference). The volume of the cylinder is (use $\pi=\dfrac{22}{7}$):
  1. $\dfrac{77}{2} \text{ cm}^{3}$
  2. $77 \text{ cm}^{3}$
  3. $11 \text{ cm}^{3}$
  4. $22 \text{ cm}^{3}$

Solution

Length becomes the circumference, breadth becomes the height. $2\pi r = 11 \Rightarrow r = \dfrac{11 \times 7}{2 \times 22} = \dfrac{7}{4}$ cm. $V = \pi r^{2} h = \dfrac{22}{7} \times \dfrac{49}{16} \times 4 = \dfrac{22 \times 49 \times 4}{7 \times 16} = \dfrac{22 \times 7}{4} = \dfrac{154}{4} = \dfrac{77}{2} = 38.5 \text{ cm}^{3}$.

Asked in: IMO

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