A cone whose height is 24 cm and radius of base is 6 cm. The volume of the cone is `:`

Options

A. `288 pi `cu cm
B. `144 pi ` cu cm
C. 200 `pi ` cu cm
D. `36 pi ` cu cm.

Answer

To find the volume of the cone, we can use the formula for the volume of a cone:

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

Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone,
- \( \pi \) is a constant approximately equal to 3.14.

### Step 1: Identify the values
From the question, we have:
- Height \( h = 24 \) cm
- Radius \( r = 6 \) cm

### Step 2: Substitute the values into the formula
Now, we can substitute the values of \( r \) and \( h \) into the volume formula:

\[ V = \frac{1}{3} \pi (6)^2 (24) \]

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

\[ r^2 = 6^2 = 36 \]

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

\[ V = \frac{1}{3} \pi (36)(24) \]

### Step 5: Multiply \( 36 \) and \( 24 \)
Next, calculate \( 36 \times 24 \):

\[ 36 \times 24 = 864 \]

### Step 6: Substitute the product back into the formula
Now substitute this product back into the volume formula:

\[ V = \frac{1}{3} \pi (864) \]

### Step 7: Divide \( 864 \) by \( 3 \)
Now, divide \( 864 \) by \( 3 \):

\[ \frac{864}{3} = 288 \]

### Step 8: Final expression for volume
Thus, the volume of the cone is:

\[ V = 288 \pi \text{ cm}^3 \]

### Final Answer
The volume of the cone is \( 288 \pi \text{ cm}^3 \).

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