Question

A pump is being used to inflate a bicycle tyre. The radius of the wheel to the centre of the tyre is 30 cm, and the mean radius of the tyre is 1.5 cm.

Estimate the volume of the tyre in m^3 (to a first approximation you can take the cross-sectional area of the tyre and multiply by the mean circumference of the wheel).

Answer 1

Let's first find the cross-sectional area of the tyre:

$$A=\pi r^2=\pi(1.5\cdot10^{-2}\ m)^2=7.1\cdot10^{-4}\ m^2.$$

Then, we can find mean circumference of the wheel:

$$C=2\pi R=2\pi\cdot0.3\ m=1.884\ m.$$

Finally, we can find the volume of the tyre:

$$V=AC=7.1\cdot10^{-4}\ m^2\cdot1.884\ m=1.34\cdot10^{-3}\ m^3.$$