Sure! Let's go through the steps needed to determine how much wallpaper Rocio needs to cover the curved surface of the cylindrical podium.
1. Identify the given dimensions of the cylinder:
- Height ([tex]\(h\)[/tex]) of the cylinder: 1.2 meters
- Diameter ([tex]\(d\)[/tex]) of the cylinder: 0.26 meters
2. Calculate the radius ([tex]\(r\)[/tex]) of the cylinder:
- The radius is half of the diameter, so:
[tex]\[
r = \frac{d}{2} = \frac{0.26}{2} = 0.13 \text{ meters}
\][/tex]
3. Find the formula for the curved surface area of a cylinder:
- The formula is given by:
[tex]\[
\text{Curved Surface Area} = 2 \pi r h
\][/tex]
where [tex]\(r\)[/tex] is the radius and [tex]\(h\)[/tex] is the height of the cylinder.
4. Substitute the known values (radius and height) into the formula:
[tex]\[
\text{Curved Surface Area} = 2 \pi (0.13) (1.2)
\][/tex]
5. Simplify the expression:
- Using the calculated values, we find that the curved surface area is approximately:
[tex]\[
\text{Curved Surface Area} \approx 0.98 \, m^2
\][/tex]
Therefore, Rocio needs approximately 0.98 square meters of wallpaper to cover the curved surface of the cylindrical podium.
The correct answer is:
B. [tex]\(0.98 \, m^2\)[/tex]
