Question

Each corner cube is removed from this $3\text{ cm}\times 3\text{ cm}\times 3\text{ cm}$ cube. The surface area of the remaining figure is

$19\text{ sq.cm}$

$24\text{ sq.cm}$

$30\text{ sq.cm}$

$54\text{ sq.cm}$

$72\text{ sq.cm}$

Solution:

Note that there is one unit cube between any pair of corner cubes, so the removal of each does not affect the others.

When we remove a corner, we are losing three unit squares. We, however, gain these back from the three faces that get uncovered.

This means that removing a corner cube does not change the surface area. The surface area of the original cube is $6 \cdot 3^2 = 6 \cdot 9 = 54$ square centimeters.

Thus, D is the correct answer.

1997 AMC 8 Problem 21

Solution:

Problem 21 in Other Years