Question

All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. 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

Answer: C

Concepts:surface area 3D geometry

Difficulty rating: 1140

Small Hint:

Cutting the cube removes some faces that were on the surface but uncovers new ones; compare the two amounts

Big Hint:

The cube’s top, front, and back faces were on the surface ( $3$ square feet removed); the notch’s floor and its two side walls become new surface ( $3$ square feet added)

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

Answer: C

Difficulty rating: 1140

Small Hint:

Big Hint:

Solution:

Problem 15 in Other Years