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.
so it is.
Now just write that in math. I assume you know what product, plus, and squared mean.
By the way, we usually write r^2 for r-squared.
Pie
To find the surface area of a cylinder with radius r and height h, we can first calculate the areas of the two circular bases, and then the area of the curved surface.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
The area of one circular base is πr^2, and since a cylinder has two circular bases, their combined area is 2πr^2.
The formula for the surface area of the curved surface (excluding the circular bases) is A = 2πrh, where A is the area, r is the radius, and h is the height.
Thus, the total surface area of the cylinder is the sum of the area of the two circular bases (2πr^2) and the curved surface area (2πrh), which can be expressed as:
Surface Area = 2πr^2 + 2πrh
According to the problem statement, this surface area is equal to twice the product of π and the square of the radius (2πr^2) plus twice the product of π, the radius, and the height (2πrh). Therefore, we can conclude that:
2πr^2 + 2πrh = 2πr^2 + 2πrh
As both sides of the equation are equal, the statement is true.