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Aright circular cylinder of maximum possible size is cut out from a solid wooden cube. The remaining material of the cube is what
percentage of the original cube? (Take = 3.14)
22.4
21.5
22.8
21.8
- You have a solid wooden cube.
- A right circular cylinder of maximum possible size is cut from it. This means the cylinder's height equals the cube's side, and its diameter equals the cube's side.
- Let the cube's side be \(s\). So, the volume of the cube is \(s^3\).
- The volume of the cylinder is \(\pi \left(\frac{s}{2}\right)^2 s = \frac{\pi s^3}{4}\).
- The remaining material is the volume of the cube minus that of the cylinder: \(s^3 - \frac{\pi s^3}{4}\).
- Simplifying, the remaining volume is \(s^3 \left(1 - \frac{\pi}{4}\right)\).
- The percentage of this remaining material is \(\left(1 - \frac{\pi}{4}\right) \times 100\%\).
- With \(\pi \approx 3.14\), calculate: \(\left(1 - \frac{3.14}{4}\right) \times 100 \approx 21.5\%\).
- Option 2: 21.5 is the correct answer.
.
By: santosh ProfileResourcesReport error
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