Answer:
Anthony must scoop out of the sink 85 cups of water to empty it
Step-by-step explanation:
The formula of the volume of a sphere is [tex]V=\frac{4}{3}\pi r^{3}[/tex] , where r is its radius
The formula of the volume of a cylinder is V = πr²h, where r is the radius of its base and h is its height
∵ The sink is shaped like a half-sphere
∵ The sink has a volume of 1072 in³
∵ One cup has a diameter of 2 in
- The radius is half the diameter
∴ The radius of the cup = [tex]\frac{1}{2}[/tex] × 2 = 1 in.
∵ The height of the cup is 4 in
- Find the volume of the cup using the 2nd formula above
∴ V = π(1)²(4) = 4π in³
To find the number of cups that Anthony use to scoop out of the sink to empty it divide the volume of the sink by the volume of the cup
∵ The volume of the sink = 1072 in³
∵ The volume of the cup = 4π in³
∴ The number of the cups = 1072 ÷ 4π
∴ The number of the cups = 85.3070495
- Round it to the nearest whole number
∴ The number of cups is 85
Anthony must scoop out of the sink 85 cups of water to empty it
