Final answer:
To find the total area of the canvas required for the circus tent, you need to calculate the area of the cylindrical part and the conical part separately. The total area is approximately 7920 m².
Step-by-step explanation:
In order to find the total area of the canvas required for the circus tent, we need to calculate the area of the cylindrical part and the conical part separately and then add them together.
Step 1: Calculate the area of the cylindrical part using the formula A_cylindrical = 2πrh, where r is the radius and h is the height of the cylinder. Since the diameter is given as 105 meters, the radius is half of that, which is 52.5 meters. The height is given as 4 meters.
A_cylindrical = 2π(52.5)(4) = 2π(210) = 420π square meters.
Step 2: Calculate the area of the conical part using the formula A_conical = πrl, where r is the radius (same as the cylindrical part) and l is the slant height. The slant height is given as 40 meters.
A_conical = π(52.5)(40) = 2100π square meters.
Step 3: Add the two areas together to get the total area of the canvas required.
Total area = A_cylindrical + A_conical = 420π + 2100π = 2520π square meters.
Finally, we can approximate the value of π as 3.14 to find the numerical value of the total area.
Total area ≈ 2520(3.14) = 7912.8 square meters.
Therefore, the answer is approximately 7920 m² (option D).