## Clock, angles and arcs

Recently we received an interesting GCSE maths question on our facebook profile. We decided to share the problem with you, as perhaps it will help someone in revising with GCSE material. The problem is as follows:

The hour hand on a clock is 12cm long. What area does it pass over in 5hrs. Take 3.142 as $\pi $

Solution to this problem is:

You are looking for area of an arc. Formula for an arc area is: $A=\pi \cdot {r}^{2}\cdot \left(\frac{C}{360\xb0}\right)$

Where r is radius, $r=12cm$

C is central angle in degrees.

If a clock passes 5hours, it means it covers 5 hours out of 12 (full circle), it means: $C=\frac{5}{12}\cdot 360\xb0=150\xb0$

Now using arc area formula: $A=3.142\cdot {12}^{2}\cdot \left(\frac{150}{360}\right)=3.142\cdot 144\cdot \left(\frac{5}{12}\right)=188.52c{m}^{2}$

We have seen similar questions where the clock passed certain amount of minutes or even seconds and the working is exactly the same. All you have to do is work out the angle and put it into the formula. On top of that, in order to help you with revision with geometry material, the following tests may be useful as well: