Question

which of the following formulas would find the lateral area of a right cylinder where ( h ) is the height and ( r ) is the radius?

a. ( la = 2pi rh )
b. ( la = 2pi r^{2} )
c. ( la = pi rh )
d. ( la = 2pi r )

Explanation:

Step1: Recall the formula for the lateral area of a right - cylinder

The lateral area of a right - cylinder is the area of the curved surface. When we "unroll" the lateral surface of a cylinder, we get a rectangle.

Step2: Determine the dimensions of the unrolled rectangle

The height of the rectangle is the height \( h \) of the cylinder. The length of the rectangle is the circumference of the base of the cylinder. The circumference of a circle is \( C = 2\pi r \).

Step3: Calculate the area of the rectangle (lateral area)

The area of a rectangle is \( A=\text{length}\times\text{height}\). Substituting the length (\( 2\pi r \)) and height (\( h \)) of the unrolled lateral surface, we get \( LA = 2\pi r\times h=2\pi rh \).

For option B, \( LA = 2\pi r^{2}\) is the formula for the combined area of the two circular bases of the cylinder (\( A = 2\times\pi r^{2}\), since the area of a single circle is \( A=\pi r^{2}\)).

For option C, \( LA=\pi rh\) is incorrect.

For option D, \( LA = 2\pi r\) is just the formula for the circumference of a circle, not an area formula.

Answer:

A. \( LA = 2\pi rh \)