Question

6. A clock has a radius of 6.2 inches. The minute hand is 5.9 inches long, and the hour hand

is 5.5 inches long.

a. How much longer is the circumference of the clock than the
circumference of the path of the tip of the minute hand? Round to
the nearest hundredth,​

Answer 1

1.89 inches

Explanation:

Circumference is basically the perimeter of a circle. This has the formula:

`C=2\pi r`

Where

C is circumference, and

r is radius

Let's find circumference of CLOCK (with radius 6.2). Shown below:

`C_(clock)=2\pi r\\C_(clock)=2\pi (6.2)\\C_(clock)=38.96`

Now, let's find circumference of tip of minute hand (with radius of minute hand being 5.9 inches). Shown below:

`C_(minute)=2\pi r\\C_(minute)=2\pi (5.9)\\C_(minute)=37.07`

The amount longer, circumference of clock is thus:

38.96 - 37.07 = 1.89 inches

Note: we have done our calculations rounding to 2 decimal places (after decimal point). This means rounding to nearest hundredth.