The area of base of a cylinder is `25picm^(2)`. If the height of cylinder is 9cm, then find the total surface area of cylinder.

Options

A. 440 cm2
B. 240 cm2
C. 420 cm2
D. 220cm2

Answer

To find the total surface area of the cylinder, we can follow these steps:

### Step 1: Understand the given information
We know that:
- The area of the base of the cylinder is \( 25\pi \, \text{cm}^2 \).
- The height of the cylinder is \( 9 \, \text{cm} \).

### Step 2: Relate the base area to the radius
The area of the base of a cylinder (which is circular) is given by the formula:
\[ \text{Area} = \pi r^2 \]
Given that the area of the base is \( 25\pi \, \text{cm}^2 \), we can set up the equation:
\[ \pi r^2 = 25\pi \]

### Step 3: Solve for the radius
To find \( r^2 \), we can divide both sides of the equation by \( \pi \):
\[ r^2 = 25 \]
Taking the square root of both sides gives:
\[ r = 5 \, \text{cm} \]

### Step 4: Use the formula for total surface area
The total surface area (TSA) of a cylinder is given by the formula:
\[ \text{TSA} = 2\pi r(h + r) \]
where \( h \) is the height of the cylinder.

### Step 5: Substitute the values into the TSA formula
Now substituting the known values:
- \( r = 5 \, \text{cm} \)
- \( h = 9 \, \text{cm} \)

We have:
\[ \text{TSA} = 2\pi(5)(9 + 5) \]
Calculating \( h + r \):
\[ h + r = 9 + 5 = 14 \]
Now substituting:
\[ \text{TSA} = 2\pi(5)(14) \]

### Step 6: Calculate the TSA
Calculating further:
\[ \text{TSA} = 2 \times 5 \times 14 \times \pi = 140\pi \]
Using \( \pi \approx \frac{22}{7} \) for calculation:
\[ \text{TSA} = 140 \times \frac{22}{7} \]
Calculating:
\[ \text{TSA} = 20 \times 22 = 440 \, \text{cm}^2 \]

### Final Answer
Thus, the total surface area of the cylinder is:
\[ \text{TSA} = 440 \, \text{cm}^2 \]