Discussion
A cylindrical glass is of capacity 100 cubic centimetre. If the radius of the glass is increased by two times of the original radius of that glass, then the capacity of the glass will be
Answer: D
The key's answer is 900 cubic centimetre.
The volume of a cylinder is \(\pi r^{2} h\), so it varies as the square of the radius when the height is unchanged. The key reads 'increased by two times of the original radius' as an increase of 2r, making the new radius 3r:
\[ \begin{aligned} V' &= 100 \times 3^{2} \\ &= 900\ \text{cm}^{3} \end{aligned} \]
If the radius were simply doubled, the volume would be \(100 \times 2^{2} = 400\) cm3, which is not offered. 200 and 600 come from treating the volume as proportional to the radius rather than its square.
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