Question 630501: The perimeter of a semicircle is doubled when the radius is increased by 3. Find the radius of the semicircle. Found 2 solutions by nerdybill, MathTherapy:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! The perimeter of a semicircle is doubled when the radius is increased by 3. Find the radius of the semicircle.
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perimeter of semicircle:
(pi)d/2 + d
in terms of r:
(pi)r/4 + 2r
r(pi/4 + 2)
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From: "perimeter of a semicircle is doubled when the radius is increased by 3" we get our equation:
2(r(pi/4 + 2)) = (r+3)(pi/4 + 2)
2(r(pi/4 + 2)) = 2(r+3)(pi/8 + 1)
r(pi/4 + 2) = (r+3)(pi/8 + 1)
r*pi/4 + 2r = rpi/8 + r + 3pi/8 +3
r*pi/4 + 2r -rpi/8 - r = 3pi/8 +3
r(pi/4 + 2 -pi/8 - 1) = 3pi/8 +3
r(pi/4 - pi/8 + 1) = 3pi/8 +3
r(2pi/8 - pi/8 + 1) = 3pi/8 +3
r(pi/8 + 1) = 3pi/8 +3
r(pi/8 + 1) = 3(pi/8 +1)
r = 3"
You can put this solution on YOUR website!
The perimeter of a semicircle is doubled when the radius is increased by 3. Find the radius of the semicircle.
Let original radius be r
Perimeter of a semicircle = ˝ circumference, plus diameter, or ˝C + D, or ˝2πr + 2r, or , or πr + 2r, or r(π + 2)
Perimeter with radius of r doubles when radius is increased by 3
2[r(π + 2)] = (r + 3)(π + 2)
2(πr + 2r) = πr + 2r + 3π + 6
2πr + 4r = πr + 2r + 3π + 6
2πr - πr + 4r – 2r = 3π + 6
πr + 2r = 3π + 6
r(π + 2) = 3(π + 2)
r, or original radius = units
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