A right cylindrical vessel is full with water. How many right cones having the same diameter and height as that of the right cylinder will be needed to store that water ? (Take `pi = (22)/(7)`).

Options

A. 4
B. 2
C. 3
D. 5

Answer

To solve the problem of how many right cones are needed to store the water from a right cylindrical vessel, we will follow these steps:

### Step 1: Understand the Volume Formulas
The volume of a right circular cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
The volume of a right circular cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]

### Step 2: Set Up the Equation
Let \( X \) be the number of cones required to store the water from the cylinder. The total volume of \( X \) cones can be expressed as:
\[ V_{\text{total cones}} = X \cdot V_{\text{cone}} = X \cdot \left( \frac{1}{3} \pi r^2 h \right) \]

### Step 3: Equate the Volumes
Since the volume of water in the cylinder must equal the total volume of the cones, we set the two volumes equal:
\[ \pi r^2 h = X \cdot \left( \frac{1}{3} \pi r^2 h \right) \]

### Step 4: Simplify the Equation
We can simplify this equation by dividing both sides by \( \pi r^2 h \) (assuming \( r \) and \( h \) are not zero):
\[ 1 = X \cdot \frac{1}{3} \]

### Step 5: Solve for \( X \)
To find \( X \), we multiply both sides by 3:
\[ X = 3 \]

### Conclusion
Thus, the number of right cones needed to store the water from the cylindrical vessel is \( 3 \).