Find the volume of the cone of height 10 cm and radius of the base 3 cm.

Answer

To find the volume of a cone with a height of 10 cm and a radius of the base of 3 cm, we can follow these steps:

### Step 1: Identify the formula for the volume of a cone.
The formula for the volume \( V \) of a cone is given by:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius of the base and \( h \) is the height of the cone.

### Step 2: Substitute the known values into the formula.
We are given:
- Height \( h = 10 \) cm
- Radius \( r = 3 \) cm

Now, substituting these values into the formula:

\[ V = \frac{1}{3} \pi (3 \, \text{cm})^2 (10 \, \text{cm}) \]

### Step 3: Calculate \( r^2 \).
First, we calculate \( r^2 \):

\[ (3 \, \text{cm})^2 = 9 \, \text{cm}^2 \]

### Step 4: Substitute \( r^2 \) back into the volume formula.
Now substitute \( r^2 \) back into the volume formula:

\[ V = \frac{1}{3} \pi (9 \, \text{cm}^2) (10 \, \text{cm}) \]

### Step 5: Multiply the values.
Now, perform the multiplication:

\[ V = \frac{1}{3} \pi (90 \, \text{cm}^3) \]

### Step 6: Simplify the expression.
Now simplify the expression:

\[ V = 30 \pi \, \text{cm}^3 \]

### Final Answer:
The volume of the cone is:

\[ V = 30 \pi \, \text{cm}^3 \]

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