Discussion
A rectangular sheet of paper 88 cm × 10 cm is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ? (Take \(\pi = \frac{22}{7}\))
Answer: B
The capacity is 6.16 litres.
The height is 10 cm, so the 88 cm side wraps round to form the circumference of the base.
\[ \begin{aligned} 2\pi r &= 88 \\ r &= \frac{88 \times 7}{2 \times 22} = 14 \text{ cm} \end{aligned} \]
\[ \begin{aligned} V &= \pi r^{2} h \\ &= \tfrac{22}{7} \times 196 \times 10 \\ &= 6160 \text{ cm}^{3} \end{aligned} \]
Since 1 litre = 1000 cm3, the capacity is 6.16 litres. The other values do not fit a radius of 14 cm and a height of 10 cm; the key step is seeing that the 88 cm edge becomes the circumference, because the 10 cm edge is the height.
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