Question

a cylinder can be modeled as a rectangle rolled up around itself. the area of a rectangle is given by the formula ( a = bh ). you want to find the area of the rectangle that surrounds the body of any given cylinder. the rectangle is the same height as the cylinder. the rectangles base has the same length as the circumference of the circle that makes up the bottom and top of the cylinder. the circumference formula is ( c = 2pi r ). which of the following best builds a function for finding the area of a rectangle in a cylinder? (1 point)

( ○ a = hr^2 )
( ○ a = 2pi rh )
( ○ a = \frac{hr}{2} )
( ○ a = \frac{h}{2r} )

Explanation:

Step1: Identify the base and height of the rectangle

The height \(h\) of the rectangle is the height of the cylinder. The base \(b\) of the rectangle is the circumference of the circular base of the cylinder. Given \(C = 2\pi r\), so \(b=2\pi r\).

Step2: Substitute into the area formula of the rectangle

The area formula of a rectangle is \(A = bh\). Substitute \(b = 2\pi r\) into it, we get \(A=(2\pi r)h=2\pi rh\).

Answer:

\(A = 2\pi rh\) (the second option)