Question

All six faces of a rectangular solid are rectangles, and the solid measures $1$ foot by $3$ feet by $9$ feet. A one-foot cube is cut out of the top of the solid to form a notch; the notch spans the full one-foot depth (from the front face to the back face) and lies partway along the nine-foot length. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?

$2$ less

$1$ less

the same

$1$ more

$2$ more

Solution:

The removed cube had three faces on the surface of the solid (top, front, and back), so $3$ square feet of surface are removed.

Cutting it out exposes three new faces (the floor of the notch and its two side walls), adding $3$ square feet. The surface area is unchanged.

Thus, the correct answer is C .

1991 AMC 8 Problem 15

Solution:

Problem 15 in Other Years