Discussion
The volume of a right circular cylinder is 554.4 cm3 and its height is 10 cm. What is the perimeter of the base of the cylinder? (Use \(\pi = \frac{22}{7}\))
Answer: B
The perimeter of the base is 26.4 cm. The volume of a cylinder is \(\pi r^{2}h\), so \[ \pi r^{2} = \frac{554.4}{10} = 55.44 \] \[ \begin{aligned} r^{2} &= 55.44\times\frac{7}{22} \\ &= 17.64 \Rightarrow r \\ &= 4.2\text{ cm} \end{aligned} \] The perimeter (circumference) of the base is \[ \begin{aligned} 2\pi r &= 2\times\frac{22}{7}\times 4.2 \\ &= 26.4\text{ cm} \end{aligned} \] The base radius of 4.2 cm gives 26.4 cm, so 17.6 cm, 22 cm and 44 cm are not the circumference of that circle. Check: \(\frac{22}{7}\times 4.2^{2}\times 10 = 554.4\), which is the given volume.
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