Question

a. Find the length of a 10° arc of a circle whose radius is 4 cm.b. Explain why the arc length in part (a) is longer or shorter in centimeters if the radius had been 6 cm.c. Find the arc length when the radius is increased to 6 cm.

Answer 1

`\begin{gathered} a)\text{ 0.7 cm} \\ b)\text{ it will be shorter as the circle with radius 6 cm is larger} \\ c)\text{ 1.05 cm} \end{gathered}`

Step-by-step explanation:

a) Here, we want to get the length of the arc

Mathematically, we can calculate that using the formula:

`L\text{ = }(\theta)/(360)\text{ }*\text{ 2}\pi r`

where r is the radius of the circle which is 5 cm

theta is the central angle subtended by the arc which is 10 degrees

Substituting the values, we have it that:

`L\text{ = }(10)/(360)\text{ }*\text{ 2}*3.142\text{ }*\text{ 4 = 0.70 cm}`

b) The arc will be shorter than the one on a circle with a radius of 6 cm

The reason for this is that a circle with a radius of 6 cm will be larger than one with a radius of 4 cm

c) Here, we want to find the length if the radius was 6 cm

We simply substitute for the radius and the central angle as we have done in (a)

We have that as:

`\begin{gathered} L\text{ = }(10)/(360)*2*3.142\text{ }*\text{ 6} \\ \\ L\text{ = 1.05 cm} \end{gathered}`