Answer:
The volume of the silo is approximately 147,026.6 ft.³.
The most correct option is 147,026.5 ft.³
Explanation:
The given dimensions of the silo are;
The shape of the silo = Composite figure of tower and roof
The shape of the tower = Cylindrical
The shape of the roof = Cone
The radius of the base of the silo, 'r' = 30 feet
The height of the cone roof of the silo, h₁ = 12 feet
The height of the entire silo = 60 feet
For the cone roof, we have;
The volume of a cone, V = 1/3 × Base area × Height
The volume of the cone roof, V₁ = 1/3×π·r² × h₁
∴ V₁ = 1/3 × π × (30 ft.)² × 12 ft. ≈ 11,309.7336 ft.³
For the cylindrical tower, we have;
The height of the entire silo = The height of the tower + The height of the roof
∴ The height of the tower = The height of the entire silo - The height of the roof
The height of the tower, h₂ = 60 ft. - 12 ft. = 48 ft.
The volume of a cylinder = Area of base × Height
The volume of the cylindrical tower, V₂ = π·r² × h₂
∴ V₂ = π × (30 ft.)² × 48 ft. ≈ 135,716.803 ft.³
The volume of the cylindrical tower, V₂ ≈ 135,716.803 ft.³
The volume of the (entire) silo, Vₙ = V₁ + V₂
∴ Vₙ = 11,309.7336 ft.³ + 135,716.803 ft.³ = 147,026.573 ft.³
The volume of the (entire) silo, Vₙ ≈ 147,026.6 ft.³.