Answer:
13) 142.4 in²
14) 6.0 cm
15) 259.4 m²
Step-by-step explanation:
Formula
[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
(where r is the radius and [tex]\theta[/tex] is in degrees)
Question 13
Given:
- r = 8 in
- [tex]\theta[/tex] = 360° - 105° = 255°
Substitute the given values into the formula and solve for A:
[tex]\implies \textsf{Area}=\left(\dfrac{255^{\circ}}{360^{\circ}}\right) \pi 8^2[/tex]
[tex]\implies \textsf{Area}=\dfrac{136}{3} \pi[/tex]
[tex]\implies \boxed{\textsf{Area}=142.4\: \sf in^2 \:(nearest\:tenth)}[/tex]
Question 14
Given:
- Area = 36 cm²
- [tex]\theta[/tex] = 114°
Substitute the given values into the formula and solve for r:
[tex]\implies 36=\left(\dfrac{114^{\circ}}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\implies \dfrac{36 \cdot 360}{114 \pi}=r^2[/tex]
[tex]\implies r^2=\dfrac{2160}{19 \pi}[/tex]
[tex]\implies r=\sqrt{\dfrac{2160}{19 \pi}}[/tex]
[tex]\implies \boxed{r=6.0\: \sf cm\:(nearest\:tenth)}[/tex]
Question 15
Given:
- Area = 49 m²
- [tex]\theta[/tex] = 68°
Substitute the given values into the formula and solve for r²:
[tex]\implies 49=\left(\dfrac{68^{\circ}}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\implies \dfrac{49 \cdot 360}{68 \pi}= r^2[/tex]
[tex]\implies r^2=\dfrac{4410}{17 \pi}[/tex]
[tex]\textsf{Area of a circle} = \pi r^2[/tex]
[tex]\implies \textsf{Area of a circle N} =\dfrac{4410}{17 \pi} \cdot \pi[/tex]
[tex]\implies \textsf{Area of a circle N} =\dfrac{4410}{17}[/tex]
[tex]\implies \boxed{\textsf{Area of a circle N} =259.4\: \sf m^2\:(nearest\:tenth)}[/tex]
