The volume of a cylinder is 900 `cm^3` . Find the volume of the cone having same radius and perpendicular height as that of cylinder.

Answer

To find the volume of the cone that has the same radius and height as the given cylinder, we can follow these steps:

### Step 1: Understand the formulas for volume
The volume \( V \) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
The volume \( V \) of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

### Step 2: Identify the known values
From the problem, we know that the volume of the cylinder is \( 900 \, \text{cm}^3 \):
\[ V_{\text{cylinder}} = 900 \, \text{cm}^3 \]
This means:
\[ \pi r^2 h = 900 \]

### Step 3: Relate the volumes of the cylinder and cone
Since the cone has the same radius \( r \) and height \( h \) as the cylinder, we can substitute the volume of the cylinder into the formula for the volume of the cone:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

### Step 4: Substitute the volume of the cylinder into the cone's volume formula
Using the equation from Step 2:
\[ V_{\text{cone}} = \frac{1}{3} \times 900 \]

### Step 5: Calculate the volume of the cone
Now, we can calculate:
\[ V_{\text{cone}} = \frac{900}{3} = 300 \, \text{cm}^3 \]

### Final Answer
The volume of the cone is:
\[ \boxed{300 \, \text{cm}^3} \]