Answer:
Okay, let's break down the problem and solve it step by step:
Understand the given information:
The pillar consists of a cylinder and a cone on top of it.
The total height of the pillar is 10.25 feet.
The height of the cylinder is 6.25 feet.
The base area of the cylinder is 47 square feet.
Calculate the height of the cone:
Height of the cone = Total height of the pillar - Height of the cylinder
Height of the cone = 10.25 feet - 6.25 feet = 4 feet
Calculate the radius of the cylinder (and the base of the cone):
Base area of the cylinder = π × radius²
47 = π × radius²
47 ÷ π = radius²
radius² = 47 ÷ π ≈ 14.96
radius = √(47 ÷ π) ≈ 3.87 feet
Calculate the slant height of the cone:
slant height² = radius² + height of the cone²
slant height² = 3.87² + 4² = 14.96 + 16 = 30.96
slant height = √30.96 ≈ 5.56 feet
Calculate the area to be painted:
Area to be painted = Curved surface area of the cylinder + Curved surface area of the cone
Curved surface area of the cylinder = 2 × π × radius × height of the cylinder
Curved surface area of the cylinder = 2 × π × 3.87 × 6.25 ≈ 152.17 square feet
Curved surface area of the cone = π × radius × slant height
Curved surface area of the cone = π × 3.87 × 5.56 ≈ 67.61 square feet
Total area to be painted = 152.17 + 67.61 ≈ 219.78 square feet
Therefore, the area to be painted on the pillar is approximately 219.78 square feet.