Final answer:
Ellie needs to paint a circular gazebo with a diameter of 13.5 meters. The radius is 6.75 meters. The area to be painted is approximately 143.1 square meters.
Step-by-step explanation:
Ellie needs to determine the area of the ceiling she will be painting, which is a circular gazebo with a diameter of 13.5 meters. The formula for the area (A) of a circle is πr², where r is the radius of the circle. Since the diameter is 13.5 meters, the radius is half of that, which is 6.75 meters. Using the formula:
A = π × (6.75 meters)²
Calculating further:
A = π × (6.75 meters × 6.75 meters)
A = π × (45.5625 m²)
When we multiply this by π (approximately 3.14159), we get:
A = 3.14159 × (45.5625 m²)
A ≈ 143.1 square meters
Therefore, Ellie will need to cover approximately 143.1 square meters of area with paint.