60 discs, each of diameter 21 cm and thickness \(\frac{1}{3}\) cm, are stacked one above the other to form a right circular cylinder. What is one-third of its volume in m3? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2.31\times10^{-3}\) m3
The stacked discs form one cylinder whose height is the total thickness of all the discs; its volume is \(\pi r^2h\). Since \(1\,\mathrm{m}=100\,\mathrm{cm}\), \(1\,\mathrm{m}^3=10^6\,\mathrm{cm}^3\).
Radius \(=21\div2=10.5\) cm
Height \(\displaystyle =60\times\frac{1}{3}=20\) cm
Volume \(\displaystyle =\frac{22}{7}\times10.5\times10.5\times20=6930\) cm3
One-third of the volume \(=6930\div3=2310\) cm3
\(2310\div10^6=2.31\times10^{-3}\) m3
Why the other options are incorrect
Option (1) \(6.93\times10^{-3}\) m3 — Incorrect. This is the whole volume of the cylinder, not one-third of it.
Option (2) \(80.05\times10^{-3}\) m3 — Incorrect. It is more than ten times the whole volume, so it cannot be a third of it.
Option (4) \(4.25\times10^{-3}\) m3 — Incorrect. It does not come from the given figures; one-third of 6930 cm3 is 2310 cm3, not 4250 cm3.