Difference between revisions of "1957 AHSME Problems/Problem 6"

(Created page with "The resulting metal piece looks something like this where the white parts are squares of length <math>x</math>: <asy> fill((0,4)--(4,4)--(4,0)--(6,0)--(6,4)--(10,4)--(10,10)-...")
 
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From here, try to visualize the rectangular prism coming together and realize the height is <math>x</math>, the length is <math>14-2x</math>, and the width is <math>10-2x</math>. Therefore, the volume is <math>x(14-2x)(10-2x)=x(4x^2-48x+40)=
 
From here, try to visualize the rectangular prism coming together and realize the height is <math>x</math>, the length is <math>14-2x</math>, and the width is <math>10-2x</math>. Therefore, the volume is <math>x(14-2x)(10-2x)=x(4x^2-48x+40)=
 
\boxed{\textbf{(A) } 140x - 48x^2 + 4x^3}</math>.
 
\boxed{\textbf{(A) } 140x - 48x^2 + 4x^3}</math>.
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{{AHSME box|year=1957|ab=B|num-b=5|num-a=7}}
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{{MAA Notice}}

Revision as of 01:05, 19 June 2019

The resulting metal piece looks something like this where the white parts are squares of length $x$:

[asy] fill((0,4)--(4,4)--(4,0)--(6,0)--(6,4)--(10,4)--(10,10)--(6,10)--(6,14)--(4,14)--(4,10)--(0,10)--cycle,grey); draw((0,0)--(14-4,0)--(10,14)--(0,14)--cycle); draw((0,0)--(0,4)--(4,4)--(4,0)--cycle); draw((10-4,0)--(10,0)--(10,4)--(6,4)--cycle); draw((0,14)--(4,14)--(4,10)--(0,10)--cycle); draw((6,14)--(6,10)--(10,10)--(10,14)--cycle); [/asy]

From here, try to visualize the rectangular prism coming together and realize the height is $x$, the length is $14-2x$, and the width is $10-2x$. Therefore, the volume is $x(14-2x)(10-2x)=x(4x^2-48x+40)= \boxed{\textbf{(A) } 140x - 48x^2 + 4x^3}$.

1957 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AHSME Problems and Solutions

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