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

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.

Answer 2

General formula to find the area of a circle
$\boxed{a= \pi \times r^{2}}$
To find a sector area of a circle
$\boxed{\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}}$

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

The area of the sector:
$\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}$
$\text{sector}= \dfrac{110^{0}}{360^{0}} \times \pi \times 12^{2}$
$\text{sector}= \dfrac{11}{36} \times \pi \times 144$
$\text{sector}= \dfrac{1584}{36} \pi$
$\text{sector}= 44 \pi$
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:
$\text{sector}= \dfrac{\text{sector in degrees}}{360^{0}} \times \pi \times r^{2}$
$\text{sector}= \dfrac{15^{0}}{360^{0}} \times \pi \times 30^{2}$
$\text{sector}= \dfrac{1}{24} \times \pi \times 900$
$\text{sector}= \dfrac{900}{24} \pi$
$\text{sector}= 37.5 \pi$
sector = 37.5 × 3.14
sector = 117.75

The area is 37.5π ≈ 117.75 yd²