Question

NO LINKS!! Find the indicated measure for each circle shown. Round answers to the nearest tenth. ​

Answer 1

Problem 13

x = central angle = 360-105 = 255 degrees

r = 8 = radius

A = sector area

A = (x/360)*pi*r^2

A = (255/360)*pi*8^2

A = 142.41887

I used the calculator's stored value of pi to get the most accuracy possible.

Round that decimal value however you need to. The same applies to the other questions as well.

Answer: Approximately 142.41887 square inches

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Problem 14

x = central angle = 114 degrees

r = radius = unknown

A = sector area = 36 square cm

A = (x/360)*pi*r^2

36 = (114/360)*pi*r^2

36*(360/114) = pi*r^2

113.68421 = pi*r^2

r^2 = 113.68421/pi

r^2 = 36.18681

r = sqrt(36.18681)

r = 6.015547

Answer: Approximately 6.015547 cm

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Problem 15

x = area of the full circle

The pizza slice shown has an area of 49 square meters.

This is 68/360 of a full circle, which means,

sector area = (68/360)*(full circle area)

49 = (68/360)*x

x = 49*(360/68)

x = 259.41176

Answer: Approximately 259.41176 square meters

Answer 2

13) 142.4 in²

14) 6.0 cm

15) 259.4 m²

Explanation:

Formula

`\textsf{Area of a sector of a circle}=\left((\theta)/(360^(\circ))\right) \pi r^2`

(where r is the radius and
`\theta` is in degrees)

Question 13

Given:

• r = 8 in
• 
  `\theta` = 360° - 105° = 255°

Substitute the given values into the formula and solve for A:

`\implies \textsf{Area}=\left((255^(\circ))/(360^(\circ))\right) \pi 8^2`

`\implies \textsf{Area}=(136)/(3) \pi`

`\implies \boxed{\textsf{Area}=142.4\: \sf in^2 \:(nearest\:tenth)}`

Question 14

Given:

• Area = 36 cm²
• 
  `\theta` = 114°

Substitute the given values into the formula and solve for r:

`\implies 36=\left((114^(\circ))/(360^(\circ))\right) \pi r^2`

`\implies (36 \cdot 360)/(114 \pi)=r^2`

`\implies r^2=(2160)/(19 \pi)`

`\implies r=\sqrt{(2160)/(19 \pi)}`

`\implies \boxed{r=6.0\: \sf cm\:(nearest\:tenth)}`

Question 15

Given:

• Area = 49 m²
• 
  `\theta` = 68°

Substitute the given values into the formula and solve for r²:

`\implies 49=\left((68^(\circ))/(360^(\circ))\right) \pi r^2`

`\implies (49 \cdot 360)/(68 \pi)= r^2`

`\implies r^2=(4410)/(17 \pi)`

`\textsf{Area of a circle} = \pi r^2`

`\implies \textsf{Area of a circle N} =(4410)/(17 \pi) \cdot \pi`

`\implies \textsf{Area of a circle N} =(4410)/(17)`

`\implies \boxed{\textsf{Area of a circle N} =259.4\: \sf m^2\:(nearest\:tenth)}`