Let’s say we have a solid cylinder, like a can. We know its radius (r) is 5cm, which means the distance from the center to the edge of the top or bottom of the can is 5cm. The height (h) of the can is 10cm, which is how tall it is from top to bottom.

Now, we want to find the total surface area of the can. To do that, we need to add up the areas of all its sides. The total surface area is given by this formula: 2πrh + 2πr^2. Let’s break it down:

First, we calculate 2πrh. The π symbol (pi) is a special number that helps us with calculations involving circles. It’s about 3.14. So, we have 2 × 3.14 × 5 × 10, which equals 314 square centimeters.

Next, we calculate 2πr^2. We multiply π by the radius squared. Squaring a number means multiplying it by itself. So, we have 2 × 3.14 × 5^2. 5^2 means 5 × 5, which equals 25. So, 2 × 3.14 × 25 is 157 square centimeters.

Now, we add those two results together: 314 + 157, which equals 471 square centimeters.

So, the total surface area of the can is 471 square centimeters.

Or

=2πr(h+r)

=2π×5(10+5)

=π×10×15

=150πcm squre