The surface area of a cylinder with radius r and height h is twice the product of pi and the square of the radius plus twice the product of pi, the radius, and the height.
See Jack's post for an example of writing the expression.
To find the surface area of a cylinder with radius r and height h, we can use the formula:
Surface Area = 2 * (π * r^2) + 2 * (π * r * h)
Let's break down the formula:
The first term, 2 * (π * r^2), represents the area of the two circular bases of the cylinder. Since the formula for the area of a circle is π * r^2, we multiply it by 2 to account for the top and bottom surfaces of the cylinder.
The second term, 2 * (π * r * h), represents the lateral surface area of the cylinder. Here, we multiply the circumference of the circle (2 * π * r) by the height (h) to calculate the surface area of the curved side of the cylinder.
By adding both terms together, we obtain the total surface area of the cylinder.
Therefore, the surface area of a cylinder with radius r and height h is given by the formula:
Surface Area = 2 * (π * r^2) + 2 * (π * r * h)
To find the formula for the surface area of a cylinder with radius r and height h, we can follow these steps:
1. The formula for the lateral surface area of a cylinder is given by multiplying the circumference of the base by the height. Since the circumference of the base is equal to 2πr, the lateral surface area can be calculated as 2πrh.
2. The formula for the area of each base of the cylinder is given by πr^2.
3. Since a cylinder has two bases, the total area of both bases can be calculated as 2πr^2.
4. The total surface area of the cylinder is the sum of the lateral surface area and the area of both bases. Therefore, the surface area equation can be written as:
Surface Area = 2πrh + 2πr^2.
So, the surface area of a cylinder with radius r and height h is equal to twice the product of π and the square of the radius plus twice the product of π, the radius, and the height, as stated in the question.