Answer:
(a) 63 cups
(b) 16 cups
Explanation:
Given that the volume of the sink = (2000/3)×π in³
(a) For the cup that has diameter = 4 in. and height, h = 8 in.
The radius, r = Diameter/2 = 4/2 = 2 in.
The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×2²×8 = (32/3)×π in.³
The number of cups to scoop = (Volume of the sink)/(Volume of the cup)
The number of cups to scoop = ((2000/3)×π)/((32/3)×π ) = 125/2=62.5 cups
Rounding to the next whole number gives 62.5 cups ≈ 63 cups
(b) For the cup that has diameter = 8 in. and height, h = 8 in.
The radius, r = Diameter/2 = 8/2 = 4 in.
The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×4²×8 = (128/3)×π in.³
The number of cups to scoop = (Volume of the sink)/(Volume of the cup)
The number of cups to scoop = ((2000/3)×π)/((128/3)×π ) = 125/8=15.625 cups
Rounding to the next whole number gives 15.625 cups ≈ 16 cups.