To determine the area of the label that needs to be printed to wrap around the cylindrical container, we need to follow these steps:
1. Calculate the radius of the cylinder:
The diameter of the cylinder is given as 5 inches. The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{5 \text{ inches}}{2} = 2.5 \text{ inches}
\][/tex]
2. Calculate the circumference of the base of the cylinder:
The circumference [tex]\( C \)[/tex] of a circle is calculated using the formula:
[tex]\[
C = 2\pi r
\][/tex]
Given that [tex]\(\pi = 3.14\)[/tex] and [tex]\( r = 2.5 \text{ inches} \)[/tex]:
[tex]\[
C = 2 \times 3.14 \times 2.5 \text{ inches}
\][/tex]
[tex]\[
C = 15.7 \text{ inches}
\][/tex]
3. Calculate the area of the label:
The label forms a rectangle that wraps around the cylinder. The width of this rectangle is the height of the cylinder, and the length is the circumference of the base of the cylinder. The area [tex]\( A \)[/tex] of the rectangle is given by:
[tex]\[
A = \text{circumference} \times \text{height}
\][/tex]
Given that the height [tex]\( h \)[/tex] of the cylinder is 9 inches and the circumference [tex]\( C \)[/tex] is 15.7 inches:
[tex]\[
A = 15.7 \text{ inches} \times 9 \text{ inches}
\][/tex]
[tex]\[
A = 141.3 \text{ square inches}
\][/tex]
Therefore, the area of the label that needs to be printed is [tex]\( 141.3 \)[/tex] square inches. The correct answer is:
D. 141.3 in[tex]\(^2\)[/tex]
