Answer:
Step-by-step explanation:
The volume of the sink is (2000/3) π in³.
The cups that she used in scooping water from the sink are conical. The formula for determining the volume of a cone is expressed as
Volume = 1/3 × πr²h
Where
r represents the radius of the cone.
h represents the vertical height of the cone.
π is a constant whose value is 3.14
From the information given,
a) considering the first cup,
Diameter of cup = 4 inches
Radius = diameter/2 = 4/2 = 2 inches
Height = 8 inches
Therefore,
Volume of cup = 1/3 × π × 2² × 8
Volume = 1/3 × π × 4 × 8
Volume = 32π/3 inches³
The number of cups needed is
2000π/3 ÷ 32π/3
= 2000π/3 × 3/32π
= 2000/32 = 62.5
Approximately 63 cups
b) considering the second cup,
Diameter of cup = 8 inches
Radius = diameter/2 = 8/2 = 4
Height = 8 inches
Therefore,
Volume of cup = 1/3 × π × 4² × 8
Volume = 1/3 × π × 16 × 8
Volume = 128π/3
The number of cups needed is
2000π/3 ÷ 128π/3
= 2000π/3 × 3/128π
= 2000/128 = 15.625
Approximately 16 cups
