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The perimeter of a square with a side of length S is equal t
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20 Oct 2018, 00:23
20 Oct 2018, 00:23
Expert Reply
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Question Stats:
73% (00:45) correct
26% (00:31) wrong based on 19 sessions
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The perimeter of a square with a side of length S is equal to the circumference of a circle. In terms of S, what is the area of the circle?
A. \(\frac{S^4}{4\pi}\)
B. \(\frac{s^2}{\pi}\)
C. \(\frac{4s^2}{\pi^2}\)
D. \(\frac{4s^2}{\pi}\)
E. \(\frac{4s}{\pi}\)
A. \(\frac{S^4}{4\pi}\)
B. \(\frac{s^2}{\pi}\)
C. \(\frac{4s^2}{\pi^2}\)
D. \(\frac{4s^2}{\pi}\)
E. \(\frac{4s}{\pi}\)
Re: The perimeter of a square with a side of length S is equal t
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20 Oct 2018, 05:57
20 Oct 2018, 05:57
1
perimeter of square , 4S
if radius r, then we have 4S= 2* pi* r => r= (2*s)/pi
so area = [4*S^2][/pi]
if radius r, then we have 4S= 2* pi* r => r= (2*s)/pi
so area = [4*S^2][/pi]
Re: The perimeter of a square with a side of length S is equal t
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28 Oct 2018, 07:55
28 Oct 2018, 07:55
Expert Reply
The perimeter of a square with a side of length S is equal to the circumference of a circle. In terms of S, what is the area of the circle?
Two ways
(I). Geometric
Perimeter of square = 4S = \(2\pi*r..........r=\frac{2S}{\pi}....Area = \pi*r^2=\pi(\frac{2S}{\pi})^2=\frac{4S^2}{\pi}\)
(II) take S as \(\pi\)
so perimeter = 4\(\pi\)=circumference = \(2\pi*r=4\pi.....r=2.......Area = \pi*r^2=4\pi\)
check choices
A. \(\frac{S^4}{4\pi}......\frac{\pi^4}{4\pi}=\pi^3/4\)...no
B. \(\frac{s^2}{\pi}.....\frac{\pi^2}{\pi}=\pi\)...no
C. \(\frac{4s^2}{\pi^2}.....\frac{4\pi^2}{\pi^2}=4\)....no
D. \(\frac{4s^2}{\pi}.......\frac{4\pi^2}{\pi}=4\pi\)...yes
E. \(\frac{4s}{\pi}.........\frac{4\pi}{\pi}=4\)....no
D
Two ways
(I). Geometric
Perimeter of square = 4S = \(2\pi*r..........r=\frac{2S}{\pi}....Area = \pi*r^2=\pi(\frac{2S}{\pi})^2=\frac{4S^2}{\pi}\)
(II) take S as \(\pi\)
so perimeter = 4\(\pi\)=circumference = \(2\pi*r=4\pi.....r=2.......Area = \pi*r^2=4\pi\)
check choices
A. \(\frac{S^4}{4\pi}......\frac{\pi^4}{4\pi}=\pi^3/4\)...no
B. \(\frac{s^2}{\pi}.....\frac{\pi^2}{\pi}=\pi\)...no
C. \(\frac{4s^2}{\pi^2}.....\frac{4\pi^2}{\pi^2}=4\)....no
D. \(\frac{4s^2}{\pi}.......\frac{4\pi^2}{\pi}=4\pi\)...yes
E. \(\frac{4s}{\pi}.........\frac{4\pi}{\pi}=4\)....no
D
