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Difference between revisions of "2008 AMC 8 Problems/Problem 21"

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==Solution==
 
==Solution==
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The slice is cutting the cylinder into two equal wedges with equal area. The cylinder's volume is <math>\pi r^2 h = \pi (4^2)(6) = 96\pi</math>. The area of the wedge is half this which is <math>48\pi \approx \boxed{\textbf{(C)}\ 151}</math>.
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The slice is cutting the cylinder into two equal wedges with equal volume. The cylinder's volume is <math>\pi r^2 h = \pi (4^2)(6) = 96\pi</math>. The volume of the wedge is half this which is <math>48\pi \approx \boxed{\textbf{(C)}\ 151}</math>.
  
 
== Video Solution by Omega Learn ==
 
== Video Solution by Omega Learn ==
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~ pi_is_3.14
 
~ pi_is_3.14
  
−
https://www.youtube.com/watch?v=q7OCpOn1abY
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https://www.youtube.com/watch?v=q7OCpOn1abY   ~David
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2008|num-b=20|num-a=22}}
 
{{AMC8 box|year=2008|num-b=20|num-a=22}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 19:54, 29 October 2023

Problem

Jerry cuts a wedge from a $6$-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?

[asy] defaultpen(linewidth(0.65)); real d=90-63.43494882; draw(ellipse((origin), 2, 4)); fill((0,4)--(0,-4)--(-8,-4)--(-8,4)--cycle, white); draw(ellipse((-4,0), 2, 4)); draw((0,4)--(-4,4)); draw((0,-4)--(-4,-4)); draw(shift(-2,0)*rotate(-d-5)*ellipse(origin, 1.82, 4.56), linetype("10 10")); draw((-4,4)--(-8,4), dashed); draw((-4,-4)--(-8,-4), dashed); draw((-4,4.3)--(-4,5)); draw((0,4.3)--(0,5)); draw((-7,4)--(-7,-4), Arrows(5)); draw((-4,4.7)--(0,4.7), Arrows(5)); label("$8$ cm", (-7,0), W); label("$6$ cm", (-2,4.7), N);[/asy]

$\textbf{(A)} \ 48 \qquad \textbf{(B)} \ 75 \qquad \textbf{(C)} \ 151\qquad \textbf{(D)} \ 192 \qquad \textbf{(E)} \ 603$

Solution

The slice is cutting the cylinder into two equal wedges with equal volume. The cylinder's volume is $\pi r^2 h = \pi (4^2)(6) = 96\pi$. The volume of the wedge is half this which is $48\pi \approx \boxed{\textbf{(C)}\ 151}$.

Video Solution by Omega Learn

https://youtu.be/FDgcLW4frg8?t=2556

~ pi_is_3.14

https://www.youtube.com/watch?v=q7OCpOn1abY ~David

See Also

2008 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 20 		Followed by
Problem 22
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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