Question

I need help on #16 and #14, when I did question 15 it was fine but I keep running into problems on how to solve 14 and 16

Answer 1

General formula to find the area of a circle

`\boxed{a= \pi * r^(2)}`
To find a sector area of a circle

`\boxed{\text{sector}= \frac{\text{sector in degrees}}{360^(0)} * \pi * r^(2)}`

NUMBER 14
Given information:
r = 12 cm
degree of sector = 110° (use the angle on the shaded area)

The area of the sector:

`\text{sector}= \frac{\text{sector in degrees}}{360^(0)} * \pi * r^(2)`

`\text{sector}= (110^(0))/(360^(0)) * \pi * 12^(2)`

`\text{sector}= (11)/(36) * \pi * 144`

`\text{sector}= (1584)/(36) \pi`

`\text{sector}= 44 \pi`
sector = 44 × 3.14
sector = 138.16

The area is 44π ≈ 138.16 cm²

NUMBER 16
Given information:
r = 30 yards
degree of sector = 15° (use the angle on the shaded area)

The area of the sector:

`\text{sector}= \frac{\text{sector in degrees}}{360^(0)} * \pi * r^(2)`

`\text{sector}= (15^(0))/(360^(0)) * \pi * 30^(2)`

`\text{sector}= (1)/(24) * \pi * 900`

`\text{sector}= (900)/(24) \pi`

`\text{sector}= 37.5 \pi`
sector = 37.5 × 3.14
sector = 117.75

The area is 37.5π ≈ 117.75 yd²

Answer 2

The area of a circle is pi*r^2.
The angles in a circle add up to 360 degrees.

Let's say I have a circle with radius 2.
The total area of the circle is pi* (2^2) = 4pi

Let's say I cut out 15 degrees of this circle. This piece is 15 out of 360 of the whole circle.

The area of this part is (15/360) * 4pi

The rest of the area is (360-15)/360 * 4pi.

I hope this helps.