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
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
\[
= 450 - 150 = 300\, \text{cm}^3
\]
