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Cord and Radii
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Ans B?
by seeing 3 right angles , we know that there are two squares in this shape.
So let's add up the two sides that are part of the cord on each square:
2(80) + 2(60) = 280
Now we need to include the length of the cord that's actually touching the circle. We can see that each of the two circles only have 3/4 of their circumference touching the cord (because of the right angle excluding 1/4 of the circle from being counted).
So we have :
(3/4)(2(80)Pi + 2(60)Pi) = (3/4)280Pi = 210Pi.
So the answer is 210Pi + 280. B.
by seeing 3 right angles , we know that there are two squares in this shape.
So let's add up the two sides that are part of the cord on each square:
2(80) + 2(60) = 280
Now we need to include the length of the cord that's actually touching the circle. We can see that each of the two circles only have 3/4 of their circumference touching the cord (because of the right angle excluding 1/4 of the circle from being counted).
So we have :
(3/4)(2(80)Pi + 2(60)Pi) = (3/4)280Pi = 210Pi.
So the answer is 210Pi + 280. B.
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My answer is (B) 210pi + 280
Here is the solution:
total length of cord = length of cord(s) between the circles + length of cord surrounding circle 1 + length of cord surrounding circle 2
Length of cord between circles = (80 + 60) + (80 + 60) = 280. [ As you can see its forming squares on both sides).
Length of cord surrounding 1st circle = circumference of circle1 - length of arc not covered
= 2 * pi * 80 - length of arc
Using the formula for length of arc
l = radius * angle covered by arc
l = 80 * pi /2
= 40 * pi
Hence Length of arc surrounding circle1 = 160 * pi - 40 * pi = 120 * pi
Repeat the same to find out for circle2
= 2 * pi * 60 - length of arc
= 120 * pi - 60 * pi/2
= 90 * pi
Add all of them
120pi + 90pi + 280 = 210pi + 280
Ans (B)
Here is the solution:
total length of cord = length of cord(s) between the circles + length of cord surrounding circle 1 + length of cord surrounding circle 2
Length of cord between circles = (80 + 60) + (80 + 60) = 280. [ As you can see its forming squares on both sides).
Length of cord surrounding 1st circle = circumference of circle1 - length of arc not covered
= 2 * pi * 80 - length of arc
Using the formula for length of arc
l = radius * angle covered by arc
l = 80 * pi /2
= 40 * pi
Hence Length of arc surrounding circle1 = 160 * pi - 40 * pi = 120 * pi
Repeat the same to find out for circle2
= 2 * pi * 60 - length of arc
= 120 * pi - 60 * pi/2
= 90 * pi
Add all of them
120pi + 90pi + 280 = 210pi + 280
Ans (B)