Question

A 3x3x3 cube has three square holes, each with a 1 by 1 cross-section running from the centre of each face to the centre of the opposite face. The total surface area (in square units) of the resulting solid is:

• A. 24
• B. 48
• C. 72
• D. 78

Answer 1

The correct option is C

72

The surface area of the solid consists of 6 faces of dimension 3 $\times$ 3 each with a 1 $\times$ 1 square hole.
The walls of the 6 holes can each be unfolded to form 1 $\times$ 4 rectangles.
Thus the surface area is 6(3$\times$3-1$\times$1)+6$\times$4 = 72