Question

The length of arc PR is 12 centimeters and its measure is 60° on circle O.Section A:A. 68.76B. 275.06C. 137.51Section B:A. 57.86B. 34.92C. 82.90

Answer 1

The length l of the arc is calculated below as

`\begin{gathered} l=(\theta)/(360)*2\pi r \\ Substitute\text{ }\theta=60^0\text{ and }l=12\text{ into the equation:} \\ 12=(60)/(360)*2\pi* r \end{gathered}`

Therefore, the value of r:

`r=11.46`

To find the area, A, of a sector, the formula is

`\begin{gathered} A=(\theta)/(360)*\pi r^2 \\ Where\text{ } \\ r=11.46\text{ cm \lparen two decimal places\rparen} \end{gathered}`

Substitute for r

`\begin{gathered} A=(60)/(360)*\pi*(11.46)^2 \\ A=68.76\text{ cm}^2\text{ } \end{gathered}`

Hence,

The area of the sector is approximately is 68.76cm²

The perimeter of the sector is given by:

`length\text{ of arc}+r+r`

Therefore, the perimeter is given by:

`12+2*11.4615\approx34.92cm`

Hence,

The perimeter of the sector is approximately 34.92cm