From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid. (Take `pi = 3.14`)

Explanation

To find the volume of the remaining solid after removing a right circular cone from a right circular cylinder, we will follow these steps:

### Step 1: Identify the dimensions of the cylinder and cone
- Height of the cylinder (h) = 10 cm
- Radius of the base (r) = 6 cm

### Step 2: Calculate the volume of the cylinder
The formula for the volume of a cylinder is given by:
\[ V_{cylinder} = \pi r^2 h \]
Substituting the values:
\[ V_{cylinder} = 3.14 \times (6)^2 \times 10 \]

### Step 3: Calculate \(6^2\)
\[ 6^2 = 36 \]

### Step 4: Substitute \(6^2\) back into the volume formula
\[ V_{cylinder} = 3.14 \times 36 \times 10 \]

### Step 5: Calculate \(36 \times 10\)
\[ 36 \times 10 = 360 \]

### Step 6: Substitute back to find the volume of the cylinder
\[ V_{cylinder} = 3.14 \times 360 \]

### Step 7: Calculate \(3.14 \times 360\)
\[ V_{cylinder} = 1130.4 \text{ cm}^3 \]

### Step 8: Calculate the volume of the cone
The formula for the volume of a cone is given by:
\[ V_{cone} = \frac{1}{3} \pi r^2 h \]
Substituting the values:
\[ V_{cone} = \frac{1}{3} \times 3.14 \times (6)^2 \times 10 \]

### Step 9: Substitute \(6^2\) into the cone volume formula
\[ V_{cone} = \frac{1}{3} \times 3.14 \times 36 \times 10 \]

### Step 10: Calculate the volume of the cone
Using the previously calculated \(36 \times 10 = 360\):
\[ V_{cone} = \frac{1}{3} \times 3.14 \times 360 \]

### Step 11: Calculate \(\frac{1}{3} \times 3.14 \times 360\)
First, calculate \(3.14 \times 360\):
\[ 3.14 \times 360 = 1130.4 \]
Now divide by 3:
\[ V_{cone} = \frac{1130.4}{3} = 376.8 \text{ cm}^3 \]

### Step 12: Find the volume of the remaining solid
The volume of the remaining solid is given by:
\[ V_{remaining} = V_{cylinder} - V_{cone} \]
Substituting the values:
\[ V_{remaining} = 1130.4 - 376.8 \]

### Step 13: Calculate the final volume
\[ V_{remaining} = 753.6 \text{ cm}^3 \]

### Final Answer
The volume of the remaining solid is \(753.6 \text{ cm}^3\).

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