Question

The volume of air in a hollow cylinder is 450 cm\(^3\). A cone of same height and radius as that of cylinder is kept inside it. The volume of empty space in the cylinder is

• A. 225 cm\(^3\)
• B. 150 cm\(^3\)
• C. 250 cm\(^3\)
• D. 300 cm\(^3\)

Answer 1

The Correct Option is D

Given:
- Volume of air in hollow cylinder = 450 cm\(^3\).
- A cone of same height and radius as cylinder is kept inside it.
- Need to find the volume of empty space inside the cylinder.

Step 1: Formulas
- Cylinder volume:\[V_{\text{cylinder}} = \pi r^2 h\]- Cone volume:\[V_{\text{cone}} = \frac{1}{3} \pi r^2 h\]where \(r\) is radius and \(h\) is height.

Step 2: Cone Volume
Cone and cylinder have same radius and height:
\[V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}}\] Given:\[V_{\text{cylinder}} = 450\, \text{cm}^3\] Therefore,\[V_{\text{cone}} = \frac{1}{3} \times 450 = 150\, \text{cm}^3\]

Step 3: Empty Space Volume
Empty space volume = Cylinder volume - Cone volume
\[= 450 - 150 = 300\, \text{cm}^3\]

Final Answer:
\[\boxed{300\, \text{cm}^3}\]