Question:
A conical chamber with the same height and base diameter is created from a solid cylinder of height 18 cm and diameter of 14 cm. The remaining solid's volume is around (take $\pi$ = 22/7):
A conical chamber with the same height and base diameter is created from a solid cylinder of height 18 cm and diameter of 14 cm. The remaining solid's volume is around (take $\pi$ = 22/7):
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If a cone is removed from a cylinder of the same dimensions, $2/3$ of the volume remains.
Updated On: Jun 26, 2026
- 1888 cm³
- 1448 cm³
- 1848 cm³
- 1998 cm³
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Volume subtraction of solids.
Step 2: Analysis
Cylinder: $h = 18, r = 14/2 = 7$.
Cone: $h = 18, r = 7$.
Remaining volume = Volume of Cylinder - Volume of Cone.
Step 3: Calculation
Vol = $\pi r^2 h - \frac{1}{3} \pi r^2 h = \frac{2}{3} \pi r^2 h$.
Vol = $\frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 18$.
Vol = $2 \times 22 \times 7 \times 6 = 1848$.
Step 4: Conclusion
The remaining volume is 1848 cm³. Final Answer: (C)
Volume subtraction of solids.
Step 2: Analysis
Cylinder: $h = 18, r = 14/2 = 7$.
Cone: $h = 18, r = 7$.
Remaining volume = Volume of Cylinder - Volume of Cone.
Step 3: Calculation
Vol = $\pi r^2 h - \frac{1}{3} \pi r^2 h = \frac{2}{3} \pi r^2 h$.
Vol = $\frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 18$.
Vol = $2 \times 22 \times 7 \times 6 = 1848$.
Step 4: Conclusion
The remaining volume is 1848 cm³. Final Answer: (C)
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