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Minchanka [31]
3 years ago
15

Find the area of a segment formed by a chord 8" long in a circle with radius of 8"

Mathematics
1 answer:
Marta_Voda [28]3 years ago
7 0
Draw 2 radii such that their endpoints on the circle are 8 inches apartconnect these points; this is the chord and it is 8 inches longthe 2 radii and the chord form an equilateral triangleeach side is 8 inches and each angle is 60 degreesfind the area of the sector formed by the 2 radiifind the area of the equilateral trianglesubtract the area of the triangle from the area of the sector and you have the area of the segment of the circlearea of the sector: A=(q/360)*∏r2A=(60/360)*∏*82A=(1/6)(∏)(64)A=(64/6)(∏)A=(32/3)(3.14159)A=33.5103 square inchesarea of the triangle:A=(√3/4)a2 where a=length of a sideA=(1.73205/4)(82)A=(1.73205/4)(64)A=(1.73205)(16)A=27.7128 square inchessubtract33.5103-27.7128=5.7975 square inchesthe area of the segment is 5.7975 square inches
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In this question the first thing that needs to be determined is the commission taken by the pizza shop and the amount of money that falls in the part of Mindy.
We already know that Mindy sells the piece of art for $15 and the pizza shop takes 15% commission on it.
Then
Commission taken by the pizza shop = (15/100) * 15
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Then amount that falls in Mindy's part = (15 - 2.25) dollars
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Initially it looks like Mindy is making a profit of $0.75 plus the pizza worth $12. So it is a fair deal for Mindy. Now coming to the part of the pizza shop owner, we find that he also gains extra $2.25 from this deal. So it is a fair deal for both the shop keeper and Mindy.
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Step-by-step explanation:

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