Difference between revisions of "2004 AMC 10A Problems/Problem 19"
(New page: ==Problem== A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete...) |
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A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet? | A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet? | ||
− | + | <asy> | |
+ | size(250);defaultpen(linewidth(0.8)); | ||
+ | draw(ellipse(origin, 3, 1)); | ||
+ | fill((3,0)--(3,2)--(-3,2)--(-3,0)--cycle, white); | ||
+ | draw((3,0)--(3,16)^^(-3,0)--(-3,16)); | ||
+ | draw((0, 15)--(3, 12)^^(0, 16)--(3, 13)); | ||
+ | filldraw(ellipse((0, 16), 3, 1), white, black); | ||
+ | draw((-3,11)--(3, 5)^^(-3,10)--(3, 4)); | ||
+ | draw((-3,2)--(0,-1)^^(-3,1)--(-1,-0.89)); | ||
+ | draw((0,-1)--(0,15), dashed); | ||
+ | draw((3,-2)--(3,-4)^^(-3,-2)--(-3,-4)); | ||
+ | draw((-7,0)--(-5,0)^^(-7,16)--(-5,16)); | ||
+ | draw((3,-3)--(-3,-3), Arrows(6)); | ||
+ | draw((-6,0)--(-6,16), Arrows(6)); | ||
+ | draw((-2,9)--(-1,9), Arrows(3)); | ||
+ | label("$3$", (-1.375,9.05), dir(260), fontsize(7)); | ||
+ | label("$A$", (0,15), N); | ||
+ | label("$B$", (0,-1), NE); | ||
+ | label("$30$", (0, -3), S); | ||
+ | label("$80$", (-6, 8), W);</asy> | ||
<math> \mathrm{(A) \ } 120 \qquad \mathrm{(B) \ } 180 \qquad \mathrm{(C) \ } 240 \qquad \mathrm{(D) \ } 360 \qquad \mathrm{(E) \ } 480 </math> | <math> \mathrm{(A) \ } 120 \qquad \mathrm{(B) \ } 180 \qquad \mathrm{(C) \ } 240 \qquad \mathrm{(D) \ } 360 \qquad \mathrm{(E) \ } 480 </math> | ||
==Solution== | ==Solution== | ||
− | {{ | + | The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base <math>3</math> and height <math>80</math>. Thus, we get <math>3\times80=240\Rightarrow\boxed{\mathrm{(C)}\ 240}</math> |
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/PYTi6qZUAPw | ||
+ | |||
+ | Education, the Study of Everything | ||
− | |||
==See also== | ==See also== | ||
+ | {{AMC10 box|year=2004|ab=A|num-b=18|num-a=20}} | ||
+ | |||
+ | [[Category:Introductory Geometry Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 14:19, 21 April 2021
Contents
Problem
A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?
Solution
The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base and height . Thus, we get
Video Solution
Education, the Study of Everything
See also
2004 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.