A right circular cylinder has radius 7 cm and height 10 cm. Another cylinder has twice the height and half the radius. The ratio of their volumes (first : second) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 : 1
The volume of a cylinder is \(\pi r^{2}h\). The radius is squared, so halving it divides the volume by 4, while doubling the height only doubles it.
First cylinder: \(\pi\times7^{2}\times10=490\pi\,\mathrm{cm^3}\)
Second cylinder (radius 3.5 cm, height 20 cm): \(\pi\times3.5^{2}\times20=245\pi\,\mathrm{cm^3}\)
Ratio of the volumes, first to second: \(490\pi:245\pi=\) 2 : 1