Question

Hello I need help on question #5… for geometry please. This is a practice sheet.

Answer 1

Given: A circle with a diameter of 19 ft and a minor sector with a central angle of 123 degrees.

Required: To find out the area of a major sector.

Explanation: The area of the sector is given by the formula

`A=(\theta)/(360)*\pi r^2`

where,

`\theta\text{ is the central angle and }r\text{ is the radius of the circle. }`

Now, the angle of the major sector (or the shaded region) can be found as follows,

`\begin{gathered} \text{ For the major sector, }\theta=360\degree-123\degree \\ =237\degree \\ r=(19)/(2)\text{ ft} \end{gathered}`

Now, the Area of the shaded region is

`A=(237)/(360)*(22)/(7)*((19)/(2))^2`

Which on simplification gives the result,

`A=186.73\text{ feet}^2`

Final Answer: The area of the shaded region is 186.73 square feet.