A cylinder can be modeled as a rectangle rolled up around itself. The area of a rectangle is given by the formula A=bh

Question

. 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=2πr
. Which of the following best builds a function for finding the area of a rectangle in a cylinder?(1 point)
Responses

A=2πrh
upper A equals Start Fraction 2 pi r over h End Fraction

A=bh2
upper A equals b h squared

A=2πrh
upper A equals 2 pi r h

A=h2πr
upper A equals Start Fraction h over 2 pi r End Fraction

Answer 1

To find the area \( A \) of the rectangle that surrounds a cylinder, you can use the formula for the area of a rectangle, which is \( A = bh \), where \( b \) is the base and \( h \) is the height.

For the cylinder:

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

Therefore, substituting the circumference for the base in the area formula, we have:

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

This can be expressed as:

\[ A = 2\pi rh \]

So, the correct choice is:

A = 2πrh.