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605-655 (Medium)|   Geometry|      
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Bunuel
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There are cogs around the circumference of a wheel and each cog is 18 Sep 2015, 09:22
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There are cogs around the circumference of a wheel and each cog is \(\frac{\pi}{16}\) centimeter wide with a space of \(\frac{\pi}{16}\) centimeter between consecutive cogs, as shown above. How many cogs of this size, with the same space between any two consecutive cogs, fit on a wheel with diameter 6 centimeters?

(A) 96
(B) 64
(C) 48
(D) 32
(E) 24

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C
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jakeqs
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There are cogs around the circumference of a wheel and each cog is 18 Sep 2015, 11:19
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If the wheel has a diameter of 6 then its circumference is
C=6*π
Since the cog and the space between cog is π/16 each section together is π/16+π/16=π/8
6*π/(π/8)=6*8=48
C
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There are cogs around the circumference of a wheel and each cog is 18 Sep 2015, 11:29
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Bunuel

There are cogs around the circumference of a wheel and each cog is \(\frac{\pi}{16}\) centimeter wide with a space of \(\frac{\pi}{16}\) centimeter between consecutive cogs, as shown above. How many cogs of this size, with the same space between any two consecutive cogs, fit on a wheel with diameter 6 centimeters?

(A) 96
(B) 64
(C) 48
(D) 32
(E) 24

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Solution: There should same number of spaces(between cogs) as the number of cogs.
So, for n cogs there will be n spaces.
So, total length n*\(\frac{\pi}{16}\) + n*\(\frac{\pi}{16}\) = π*d ==> n=48.

Option C
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There are cogs around the circumference of a wheel and each cog is 18 Sep 2015, 12:02
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Bunuel

There are cogs around the circumference of a wheel and each cog is \(\frac{\pi}{16}\) centimeter wide with a space of \(\frac{\pi}{16}\) centimeter between consecutive cogs, as shown above. How many cogs of this size, with the same space between any two consecutive cogs, fit on a wheel with diameter 6 centimeters?

(A) 96
(B) 64
(C) 48
(D) 32
(E) 24

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76.JPG
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One cog is \(\frac{\pi}{16}\) cm wide and each space is \(\frac{\pi}{16}\) cm wide.
So, width of a set of 1 cog and 1 empty space between cogs will be \(\frac{\pi}{16}\)*2 = \(\frac{\pi}{8}\) cm
Number of such sets in a wheel of diameter 6 cm will be \(\frac{{\pi}*Diameter}{\frac{\pi}{8}}\) = \(\frac{{\pi}*6}{\frac{\pi}{8}}\) = 48

Answer:-C
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There are cogs around the circumference of a wheel and each cog is 19 Sep 2015, 00:45
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Bunuel

There are cogs around the circumference of a wheel and each cog is \(\frac{\pi}{16}\) centimeter wide with a space of \(\frac{\pi}{16}\) centimeter between consecutive cogs, as shown above. How many cogs of this size, with the same space between any two consecutive cogs, fit on a wheel with diameter 6 centimeters?

(A) 96
(B) 64
(C) 48
(D) 32
(E) 24
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Ans: C

Solution: On a circle when we put all the cogs with same spacing we will get same no. of cogs and spacing. so if there are n cogs then n spaces will be there.
total circumference of the circle = n*(width of congs + width of space)
2* pi*3= n(pi/16 + pi/16)
n= 48
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There are cogs around the circumference of a wheel and each cog is 19 Sep 2015, 03:30
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Circumference of Wheel = 2\(\pi\)r = 6\(\pi\)
Total Number of Cogs = Circumference/2*Diameter of Cog = 96\(\pi\)/2\(\pi\) = 48.

Hence Answer is. C (48)
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There are cogs around the circumference of a wheel and each cog is 19 Sep 2015, 03:39
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answer is 48

distance between two consecutive cogs is pi/8
as perimeter= 6pi

6pi/pi/8= 48
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There are cogs around the circumference of a wheel and each cog is 06 Sep 2025, 20:32
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