Answer:
The area of the bigger lid is approximately 29.2 square inches
Step-by-step explanation:
The given data are;
The volume held by one of the cans of paint, V₁ = 64 oz
The volume held by the other cans of paint, V₂ = 125 oz
The area of the smaller lid = 18 in²
Therefore,
The 64 Oz = The smaller can of paint
The 125 oz = The larger can of paint
The diameter of the smaller lid, d₁ = √(18 × 4/π) ≈ 4.787
The ratio of can volumes = (The ratio of can diameters)³
V₁/V₂ = (d₁/d₂)³
V₁/V₂ = 64/125
d₁/d₂ ≈ 4.787/d₂
64/125 = (4.787/d₂)³
4.787/d₂ = ∛(64/125) = 4/5
d₂ ≈ 4.878×5/4 = 6.0975
The area of the bigger lid, A₂ = π·d₂²/4
∴ A₂ = π × 6.0975²/4 ≈ 29.2
The area of the bigger lid, A₂ ≈ 29.2 in.²
