Question

A cube has edge length $2.$ Suppose that we glue a cube of edge length $1$ on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to

$10$

$15$

$17$

$21$

$25$

Solution:

The original surface area is just $6 \cdot 2^2 = 6 \cdot 4 = 24.$

Note that the top face of the unit cube plus the visible area of the top face of the larger cube is the same as the area of one face of the larger cube.

This means that the unit square on top only adds $4$ unit squares to the total surface area, making the increase $4.$

The percent increase is therefore $100 \cdot \dfrac{4}{24} = 100 \cdot \dfrac{1}{6} \approx 16.7\%.$

Thus, C is the correct answer.

2000 AMC 8 Problem 22

Solution:

Problem 22 in Other Years