Question

The minute hand of a clock extends out to the edge of the clock's face, which is a circle of radius 4 inches. What area does the minute hand sweep out between 9:15 and9:35? Round your answer to the nearest hundredth.

Answer 1

To solve the question, we have to make use of the fact that

A minute hand travels 360 degrees in 60 min

From the question given, we are told that the minute hand sweep out between 9:15 and

9:35, thus

There are 20 minutes in between 9:15 and 9:35

Thus

We can get the area using the formula

$\begin{gathered} Area=\frac{\text{minutes turned}}{60}\times\pi r^2 \\ \text{where} \\ r=4\text{ inches} \end{gathered}$

Area will be

$\begin{gathered} \text{Area}=\frac{20}{60}\times\pi\times4^2 \\ \text{Area}=\frac{1}{3}\times\pi\times16 \\ \text{Area}=16.755 \end{gathered}$

Thus, the area will be 16.76 in²