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2 cans of paint hold 64 and 125 oz. if the cans are similar cylinders and the smaller lid has an area of 18 find the area of the bigger lid.

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Answer:

The area of the bigger lid is approximately 29.2 square inches

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

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