Answer:
The second similar can with a radius of 24-inch radius will hold 12 gallons
Step-by-step explanation:
The given parameters are;
The volumes of the cylindrical can ∝ (The radius of the cans)³
The volume of first can, V₁ = 1¹/₂ pints
The radius of the first can, r₁ = 6-inch
The radius of the second can, r₂ = 24-inch
Therefore, we have;
V ∝ r³
V = k × r³
∴ 1¹/₂ pints ∝ (6 in.)³
1¹/₂ pints = 43.3125 in³
∴ 43.3125 in³ = k × 216 in.³
The constant of proportionality, k = 43.3125/216 = 0.2005208333
Therefore, we have for the second can, we have;
V₂ = k × r₂³ = 43.3125/216 × (24 in.)³ = 2772 in.³
The volume of the second can = 2772 in.³
1 in.³ = 0.004329 gallons
∴ 2772 in.³ = 2772 × 0.004329 gallons = 12 gallons
Therefore, the volume the second similar can with a 24-inch radius will hold = 12 gallons.
