Geometry and TrigonometryVery hardCube with a cylindrical hole
Geometry and Trigonometry practice question
A cube with edge length 6 has a cylindrical hole of radius 1 drilled straight through from one face to the opposite face. The remaining volume can be written as a − bπ, where a and b are constants. What is the value of a + b?
Answer: 222
The cube's volume is 216 and the hole's is π(1)²(6) = 6π, so the remainder is 216 − 6π and a + b = 222.
Common wrong answers
- If you answered 210
- 210 subtracts 6 without the π.
- If you answered 217
- 217 uses a hole of volume π, forgetting the height 6.
- If you answered 222π
- The question asks for a + b as a number.
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