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: Recall volume formulas
- Volume of cylinder: \[ V_{\text{cylinder}} = \pi r^2 h \] - Volume of cone: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] where \(r\) is radius and \(h\) is height.

Step 2: Find volume of cone in terms of cylinder volume
Since 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: Calculate volume of empty space
Empty space volume = Volume of cylinder - Volume of cone
\[ = 450 - 150 = 300\, \text{cm}^3 \]

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