A formula for the volume of a right circular cone is `V = 1/3 pi r^(2) h`, where r is the radius of the base and h is the height of the cone. Using `22/7` as an approximate value for `pi`, which of the following values is closest to the volume, in cubic inches, of a cone with height 28 inches and radius 6 inches?

Options

A. 264
B. 352
C. 1056
D. 4224

Answer

To find the volume of a right circular cone using the formula \( V = \frac{1}{3} \pi r^2 h \), we will follow these steps:

### Step 1: Identify the values of \( r \) and \( h \)
Given:
- Radius \( r = 6 \) inches
- Height \( h = 28 \) inches

### Step 2: Substitute the values into the formula
We will substitute the values of \( r \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Substituting \( r = 6 \) and \( h = 28 \):
\[ V = \frac{1}{3} \pi (6)^2 (28) \]

### Step 3: Calculate \( r^2 \)
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:
\[ V = \frac{1}{3} \pi (36) (28) \]

### Step 5: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{1}{3} \left(\frac{22}{7}\right) (36) (28) \]

### Step 6: Simplify the expression
Now we will simplify the expression:
\[ V = \frac{1}{3} \times \frac{22}{7} \times 36 \times 28 \]

### Step 7: Calculate \( 36 \times 28 \)
Calculate \( 36 \times 28 \):
\[ 36 \times 28 = 1008 \]
Now substitute this value back:
\[ V = \frac{1}{3} \times \frac{22}{7} \times 1008 \]

### Step 8: Calculate \( \frac{1008}{3} \)
Calculate \( \frac{1008}{3} \):
\[ \frac{1008}{3} = 336 \]
Now substitute this value back:
\[ V = \frac{22}{7} \times 336 \]

### Step 9: Multiply \( 22 \times 336 \)
Calculate \( 22 \times 336 \):
\[ 22 \times 336 = 7392 \]
Now substitute this value back:
\[ V = \frac{7392}{7} \]

### Step 10: Divide \( 7392 \) by \( 7 \)
Now divide \( 7392 \) by \( 7 \):
\[ 7392 \div 7 = 1056 \]

### Final Volume
Thus, the volume \( V \) of the cone is approximately:
\[ V \approx 1056 \text{ cubic inches} \]