Difference between revisions of "1988 AJHSME Problems/Problem 13"

(New page: ==Problem== If rose bushes are spaced about <math>1</math> foot apart, approximately how many bushes are needed to surround a circular patio whose radius is <math>12</math> feet? <math>\...)
 
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==Problem==
 
==Problem==
  
If rose bushes are spaced about <math>1</math> foot apart, approximately how many bushes are needed to surround a circular patio whose radius is <math>12</math> feet?
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If rose bushes are spaced about <math>1</math> foot apart, approximately how many bushes are needed to surround a [[circle|circular]] patio whose radius is <math>12</math> feet?
  
 
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 38 \qquad \text{(C)}\ 48 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 450</math>
 
<math>\text{(A)}\ 12 \qquad \text{(B)}\ 38 \qquad \text{(C)}\ 48 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 450</math>
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==Solution==
 
==Solution==
  
The circumference of the patio is <math>2\cdot 12\cdot \pi =24\pi \approx 75.398</math>.  Since the bushes are spaced <math>1</math> foot apart, about <math>75\rightarrow \boxed{\text{D}}</math> are needed.
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The [[circumference]] of the patio is <math>2\cdot 12\cdot \pi =24\pi \approx 75.398</math>.  Since the bushes are spaced <math>1</math> foot apart, about <math>75\rightarrow \boxed{\text{D}}</math> are needed.
  
 
==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
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{{AJHSME box|year=1988|num-b=12|num-a=14}}
 
[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Geometry Problems]]

Revision as of 06:23, 3 June 2009

Problem

If rose bushes are spaced about $1$ foot apart, approximately how many bushes are needed to surround a circular patio whose radius is $12$ feet?

$\text{(A)}\ 12 \qquad \text{(B)}\ 38 \qquad \text{(C)}\ 48 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 450$

Solution

The circumference of the patio is $2\cdot 12\cdot \pi =24\pi \approx 75.398$. Since the bushes are spaced $1$ foot apart, about $75\rightarrow \boxed{\text{D}}$ are needed.

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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All AJHSME/AMC 8 Problems and Solutions
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