Difference between revisions of "2012 AMC 8 Problems/Problem 21"
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| + | ==Problem== | ||
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet? | Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet? | ||
| − | |||
<math> \textbf{(A)}\hspace{.05in}5\sqrt2\qquad\textbf{(B)}\hspace{.05in}10\qquad\textbf{(C)}\hspace{.05in}10\sqrt2\qquad\textbf{(D)}\hspace{.05in}50\qquad\textbf{(E)}\hspace{.05in}50\sqrt2 </math> | <math> \textbf{(A)}\hspace{.05in}5\sqrt2\qquad\textbf{(B)}\hspace{.05in}10\qquad\textbf{(C)}\hspace{.05in}10\sqrt2\qquad\textbf{(D)}\hspace{.05in}50\qquad\textbf{(E)}\hspace{.05in}50\sqrt2 </math> | ||
==Solution== | ==Solution== | ||
| − | + | If Marla evenly distributes her <math>300</math> square feet of paint between the 6 faces, each face will get <math>300\div6 = 50</math> square feet of paint. The surface area of one of the faces of the cube is <math>10^2 = 100 </math> square feet. Therefore, there will be <math>100-50 = \boxed{\textbf{(D)}\ 50} </math> square feet of white on each side. | |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2012|num-b=20|num-a=22}} | {{AMC8 box|year=2012|num-b=20|num-a=22}} | ||
| + | {{MAA Notice}} | ||
Revision as of 20:00, 10 October 2016
Problem
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?
Solution
If Marla evenly distributes her 
square feet of paint between the 6 faces, each face will get 
square feet of paint. The surface area of one of the faces of the cube is 
square feet. Therefore, there will be 
square feet of white on each side.
See Also
| 2012 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
