**Problem:**

A closed circular cylinder has a diameter of 10 cm and a height of 15 cm. Find the total surface area of the cylinder. (Take π = 3.14).

**Solution:**

To find the total surface area of a closed circular cylinder, we need to calculate the areas of the two circular bases and the lateral surface area.

**1. Calculate the area of the circular bases:**

The circular bases of the cylinder are congruent, and their area can be calculated using the formula:

Area of a circle = π * radius^2

Given that the diameter is 10 cm, the radius (r) can be calculated by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 10 cm / 2 = 5 cm

Now, we can calculate the area of one circular base using the formula:

Area of circular base = π * r^2 = 3.14 * 5^2 = 3.14 * 25 = 78.5 cm^2

Since there are two circular bases, the total area of the bases is:

Total area of bases = 2 * Area of circular base = 2 * 78.5 = 157 cm^2

**2. Calculate the lateral surface area:**

The lateral surface area of a cylinder can be calculated by finding the product of the circumference of the base and the height of the cylinder.

Circumference of a circle = 2 * π * radius

Circumference of the base = 2 * 3.14 * 5 = 31.4 cm

Now, we can calculate the lateral surface area using the formula:

Lateral surface area = Circumference of base * height = 31.4 * 15 = 471 cm^2

**3. Calculate the total surface area:**

The total surface area of a cylinder is the sum of the areas of the two circular bases and the lateral surface area.

Total surface area = Total area of bases + Lateral surface area
= 157 cm^2 + 471 cm^2
= 628 cm^2

Therefore, the total surface area of the given cylinder is 628 cm^2.

Diameter of the cylinder = 10cm

radius of the cylinder = 5 cm

height of the cylinder = 15 cm

TSA of the cylinder = 2pi x r x h

                                 = 2 x 3.14 x 5 x 15

                                  =  471 cm square