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 rectangle's 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=2(pi)r. Which of the following best builds a function for finding the area of a rectangle in a cylinder?

Question

1)A=2(pi)rh
2)A=[2(pi)rh]/[h]
3)A=[h]/[2(pi)r]
4)a=bh^2

Answer 1

To find the area of the rectangle that surrounds a cylinder, we need to use the formula for the area of a rectangle, which is \( A = b \times h \), where \( b \) is the base (width) of the rectangle and \( h \) is the height.

In this case:

• The height \( h \) of the rectangle is the same as the height of the cylinder.
• The base \( b \) of the rectangle corresponds to the circumference of the cylinder, which is given by the formula \( C = 2 \pi r \).

So, the area of the rectangle can be expressed as:

\[ A = b \times h = (2 \pi r) \times h \]

Thus, we can represent this as:

\[ A = 2 \pi r h \]

Now, let's look at the given options:

1. \( A = 2 \pi rh \)
2. \( A = \frac{2 \pi rh}{h} \)
3. \( A = \frac{h}{2 \pi r} \)
4. \( A = bh^2 \)

The best option that correctly represents the area of the rectangle surrounding the cylinder is:

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