Geometry and TrigonometryVery hardVolume remaining after a hole is drilled
Geometry and Trigonometry practice question
A cube has edges of length 4. A cylindrical hole of radius 1 is drilled straight through the cube from the centre of one face to the centre of the opposite face. What is the volume of the solid that remains?
- A. 64 − 4πCorrect
- B. 64 − π
- C. 64 − 16π
- D. 60
Answer: A. 64 − 4π
Cube volume: 4³ = 64. The hole is a cylinder of radius 1 and height 4 (the full edge): π(1²)(4) = 4π. Remaining: 64 − 4π.
Why the other answers are wrong
- B. 64 − π
- π is the area of the hole's circular cross-section; the removed VOLUME multiplies that by the length of the hole, 4.
- C. 64 − 16π
- 16π uses the cube's edge as the radius. The hole's radius is 1, so its cross-section is π, and the volume is 4π.
- D. 60
- 60 treats the hole's volume as 4 instead of 4π.
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.