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 $\pi=\dfrac{22}{7}$):
$\dfrac{77}{2} \text{ cm}^{3}$
$77 \text{ cm}^{3}$
$11 \text{ cm}^{3}$
$22 \text{ cm}^{3}$
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. $V = \pi r^{2} h = \dfrac{22}{7} \times \dfrac{49}{16} \times 4 = \dfrac{22 \times 49 \times 4}{7 \times 16} = \dfrac{22 \times 7}{4} = \dfrac{154}{4} = \dfrac{77}{2} = 38.5 \text{ cm}^{3}$.