Discussion
Height of a right circular cylinder is 6 m. If three times the sum of the areas of its two circular bases is twice its curved surface area, then volume of the cylinder (in m3) is :
Answer: A
The volume is 96π m3.
Three times the area of the two bases equals twice the curved surface area:
\[ \begin{aligned} 3 \times 2\pi r^{2} &= 2 \times 2\pi r h \\ 6\pi r^{2} &= 4\pi r h \\ r &= \tfrac{2}{3}h = \tfrac{2}{3} \times 6 = 4\ \text{m} \end{aligned} \]
\[ \begin{aligned} V &= \pi r^{2} h = \pi \times 16 \times 6 \\ &= 96\pi\ \text{m}^{3} \end{aligned} \]
Using the area of only one base gives \(r = 8\) and a volume of \(384\pi\), which is not offered. The other options correspond to radii that do not satisfy the stated condition.
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