Question

An artist has $14$ cubes, each with an edge of $1$ 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?

$21$

$24$

$33$

$37$

$42$

Answer: C

Concepts:surface area cube geometry

Difficulty rating: 1050

Small Hint:

Count the exposed faces on the four vertical sides, then the faces seen from directly above

Big Hint:

Each of the four sides shows $6$ exposed faces, and looking straight down covers the full $3 \times 3$ footprint of top faces

Solution:

Because each higher layer is flush into one corner, each of the four vertical sides shows a stepped profile of $3 + 2 + 1 = 6$ exposed square faces, for $4 \times 6 = 24$ side faces.

Viewed from directly above, the top faces cover the full $3 \times 3$ footprint, adding $9$ more faces. The bottom rests on the ground and is not painted, so the total is $24 + 9 = 33$ square meters.

Thus, the correct answer is C .

1989 AMC 8 Problem 23

Answer: C

Difficulty rating: 1050

Small Hint:

Big Hint:

Solution:

Problem 23 in Other Years