the lateral ara of a right cylinder can found can be found by multiplying twice the number pie by the radius the height. If a right cylinder has radius r and height h, write an expression that represents the lateral area.

LA = 2pi * r * h

Please note that pi = 3.14

Pie = something good that you eat for dessert.

The lateral area of a right cylinder can be found by multiplying twice the value of pi by the radius and the height.

Therefore, the expression that represents the lateral area of a right cylinder with radius r and height h is:

2πrh

To find the lateral area of a right cylinder, you can use the formula: Lateral Area = 2πrh, where r represents the radius of the cylinder and h represents the height of the cylinder.

To derive this formula, let's break it down step by step:

1. The lateral area of a cylinder refers to the total surface area excluding the base and top. Since a cylinder has two identical circular bases, we need to subtract the areas of both bases from the total surface area to get the lateral area.

2. The circumference of a circle is given by 2πr, where r is the radius. Thus, the combined circumference of both bases is 2πr + 2πr = 4πr.

3. When the cylinder is "unwrapped" and presented as a rectangle, the base circumference (4πr) becomes the length (l) of the rectangle. The width (w) of the rectangle is given by the height (h) of the cylinder.

4. The lateral area of the rectangle is calculated by multiplying the length (l) and width (w), which gives us lw = (4πr)h = 4πrh.

Therefore, the expression that represents the lateral area of a right cylinder is 2πrh.

answer