Test 4 Section 4 Number 18

Test 1 #35 (calculator section)

The cube above is made from 27 small cubes, each with an edge of length 1. If the shaded cube is removed what will be the surface area of the remaining solid?

Each of the 8 edges of a pyramid with a square base is 4 inches long and each edge of a cube is 4 inches long. The base of the pyramid is set on one face of the cube so that their vertices coincide. The new solid that is formed has how many faces?

A cube with edge of length 4 is divided into 8 identical cubes. How much greater is the combined surface area of the 8 smaller cubes than the surface area of the original cube?

A) 48

B) 56

C) 96

D) 288

E) 384

A large cube with edge of length 3 units is built from 6 small blue unit cubes and 21 small white unit cubes. What is the greatest possible fraction of the surface area of the large cube that could be blue?

A) 1/9

B) 2/9

C) 1/3

D) 4/9

E) 2/3

I’m having a lot of fun playing around with some geometry drawing software this week (nyeeerd!), so I figured I’d use it again to make another “fun” 3-D problem for the weekend challenge. This is a bit tougher than you’d find on the SAT, but the underlying concepts, as always, are important for the SAT. (more…)

It’s not uncommon for a question or two involving three-dimensional shapes to appear on the SAT. Luckily, most of the time these questions either deal directly with the simple properties of three-dimensional shapes (like surface area and volume), or are just 2-D questions in disguise. It’s pretty rare to come across a truly difficult 3-D (more…)