Geometry and TrigonometryVery hardSurface area after cutting a cube
Geometry and Trigonometry practice question
A cube with edges of length 3 is cut into 27 cubes with edges of length 1. What is the total surface area of all 27 small cubes combined?
Answer: 162
Each small cube has 6 faces of area 1, so 6 square units each. 27 cubes: 27 × 6 = 162. (Cutting exposes new faces; the original cube had only 54.)
Common wrong answers
- If you answered 27
- 27 is the number of small cubes, which is also the total volume.
- If you answered 54
- 54 is the surface area of the ORIGINAL cube (6 × 3²). Cutting it exposes many new faces.
- If you answered 108
- 108 is 54 × 2, doubling the original surface; the cut cubes have three times the original area.
More Geometry and Trigonometry questions
- Very hard
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is N… - Very hard
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the valu… - Very hard
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Very hard
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Very hard
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this c… - Very hard
What is the perimeter of triangle ABC?
Not affiliated with the College Board. SAT is a trademark of the College Board.