To find out how much wallpaper Rocio needs to cover the curved surface of the cylindrical podium, we will calculate the lateral (curved) surface area of the cylinder.
The formula for the lateral surface area [tex]\(A\)[/tex] of a cylinder is given by:
[tex]\[ A = 2 \pi r h \][/tex]
where:
- [tex]\(r\)[/tex] is the radius of the cylinder,
- [tex]\(h\)[/tex] is the height of the cylinder,
- [tex]\(\pi\)[/tex] is a constant (approximately 3.14159).
First, we need to determine the radius of the cylinder. The radius [tex]\(r\)[/tex] is half of the diameter.
Given:
- The diameter of the podium is [tex]\(0.26\)[/tex] meters.
So,
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{0.26}{2} = 0.13 \, \text{meters} \][/tex]
Next, we know the height [tex]\(h\)[/tex] of the podium is [tex]\(1.2\)[/tex] meters.
Now we can substitute the values of [tex]\(r\)[/tex] and [tex]\(h\)[/tex] into the formula:
[tex]\[ A = 2 \pi r h \][/tex]
[tex]\[ A = 2 \pi (0.13) (1.2) \][/tex]
Let's compute this step by step:
[tex]\[ 2 \pi (0.13) (1.2) \approx 2 \times 3.14159 \times 0.13 \times 1.2 \][/tex]
First, calculate [tex]\(2 \times 3.14159 = 6.28318\)[/tex].
Then,
[tex]\[ 6.28318 \times 0.13 \approx 0.8168134 \][/tex]
Finally,
[tex]\[ 0.8168134 \times 1.2 \approx 0.98017608 \][/tex]
Rounding to two decimal places:
[tex]\[ 0.98017608 \approx 0.98 \][/tex]
Therefore, the amount of wallpaper Rocio needs is approximately [tex]\(0.98 \, m^2\)[/tex].
The correct answer is B. [tex]$0.98 m^2$[/tex].
