40 circular plates each of radius 7 cm and thickness 1.5 cm are placed one above the other to form a solid right circular cylindr. Find the total surface area and volume of cylinder so formed.

Answer

To solve the problem of finding the total surface area and volume of a solid right circular cylinder formed by stacking 40 circular plates, each with a radius of 7 cm and a thickness of 1.5 cm, we can follow these steps:

### Step 1: Identify the dimensions of the cylinder
- **Radius (r)** of the cylinder is the same as the radius of the plates:
\[ r = 7 \text{ cm} \]
- **Height (h)** of the cylinder is the total thickness of the 40 plates:
\[ h = \text{thickness of one plate} \times \text{number of plates} = 1.5 \text{ cm} \times 40 = 60 \text{ cm} \]

### Step 2: Calculate the total surface area of the cylinder
The formula for the total surface area (TSA) of a cylinder is given by:
\[ \text{TSA} = 2\pi r(h + r) \]
Substituting the values of \(r\) and \(h\):
- First, calculate \(h + r\):
\[ h + r = 60 \text{ cm} + 7 \text{ cm} = 67 \text{ cm} \]
- Now substitute into the TSA formula:
\[ \text{TSA} = 2 \times \frac{22}{7} \times 7 \times 67 \]
- Simplifying:
\[ \text{TSA} = 2 \times 22 \times 67 = 44 \times 67 = 2948 \text{ cm}^2 \]

### Step 3: Calculate the volume of the cylinder
The formula for the volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]
Substituting the values of \(r\) and \(h\):
- First, calculate \(r^2\):
\[ r^2 = 7^2 = 49 \text{ cm}^2 \]
- Now substitute into the volume formula:
\[ V = \frac{22}{7} \times 49 \times 60 \]
- Simplifying:
\[ V = 22 \times 60 = 1320 \text{ cm}^3 \]

### Final Results
- Total Surface Area = \(2948 \text{ cm}^2\)
- Volume = \(1320 \text{ cm}^3\)