What is the difference between the total surface area and curved surface area of a cylinder whose radius is equal to 10 cm ?

Options

A. `200 picm^(2)`
B. `300 picm^(2)`
C. `100 picm^(2)`
D. `10 picm^(2)`

Answer

To find the difference between the total surface area and the curved surface area of a cylinder with a radius of 10 cm, we can follow these steps:

### Step 1: Understand the formulas
The formulas we need are:
- Curved Surface Area (CSA) of a cylinder: \( CSA = 2\pi rh \)
- Total Surface Area (TSA) of a cylinder: \( TSA = 2\pi r(h + r) \)

Here, \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Identify the given values
From the problem, we know:
- Radius \( r = 10 \) cm
- Height \( h \) is not provided, so we will keep it as \( h \).

### Step 3: Calculate the Curved Surface Area
Using the formula for the curved surface area:
\[ CSA = 2\pi rh = 2\pi (10)h = 20\pi h \text{ cm}^2 \]

### Step 4: Calculate the Total Surface Area
Using the formula for the total surface area:
\[ TSA = 2\pi r(h + r) = 2\pi (10)(h + 10) = 20\pi(h + 10) \text{ cm}^2 \]

### Step 5: Find the difference between TSA and CSA
Now, we can find the difference:
\[ \text{Difference} = TSA - CSA = [20\pi(h + 10)] - [20\pi h] \]
\[ = 20\pi(h + 10 - h) = 20\pi(10) = 200\pi \text{ cm}^2 \]

### Final Answer
The difference between the total surface area and the curved surface area of the cylinder is \( 200\pi \text{ cm}^2 \).

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