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.
<h3>Answer: Approximately 142.41887 square inches</h3>
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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
<h3>Answer: Approximately 6.015547 cm</h3>
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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
<h3>Answer: Approximately 259.41176 square meters</h3>