There are cogs around the circumference of a wheel and each cog is

Question

https://gmatclub.com/forum/download/file.php?id=27857 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 76.JPG

jakeqs · Answer

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

anudeep133 · Answer

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

kunal555 · Answer

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

D3N0 · Answer

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

scorpionkapoor77 · Answer

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)

longfellow · Answer

answer is 48

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

6pi/pi/8= 48

bumpbot · Answer

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There are cogs around the circumference of a wheel and each cog is

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