1989 AJHSME Problems/Problem 23
Revision as of 01:11, 12 June 2009 by 5849206328x (talk | contribs) (New page: ==Problem== An artist has <math>14</math> cubes, each with an edge of <math>1</math> meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surfa...)
Problem
An artist has cubes, each with an edge of
meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?
Solution
We can consider the contributions of the sides of the three layers and the tops of the layers separately.
Layer (counting from the top starting at
) has
side faces each with
unit squares, so the sides of the pyramid contribute
for the surface area.
The tops of the layers when combined form the same arrangement of unit cubes as the bottom of the pyramid, which is a square, hence this contributes
for the surface area.
Thus, the artist paints square meters.
Solution
1989 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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