If the height of a cone is equal to diameter of its base, the volume of cone is______.

Answer

To find the volume of a cone when the height is equal to the diameter of its base, we can follow these steps:

### Step 1: Understand the relationship between height and radius
Given that the height (h) of the cone is equal to the diameter of its base, we can express this relationship mathematically.
- Let the radius of the base of the cone be \( r \).
- The diameter of the base is \( 2r \).
- According to the problem, the height \( h \) is equal to the diameter, so:
\[ h = 2r \]

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

### Step 3: Substitute the height in the volume formula
Now, we substitute the value of \( h \) from Step 1 into the volume formula:
\[ V = \frac{1}{3} \pi r^2 (2r) \]

### Step 4: Simplify the expression
Now, we simplify the expression:
\[ V = \frac{1}{3} \pi r^2 \cdot 2r = \frac{2}{3} \pi r^3 \]

### Step 5: Final expression for the volume
Thus, the volume of the cone when the height is equal to the diameter of its base is:
\[ V = \frac{2}{3} \pi r^3 \text{ cubic units} \]