Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of (2000/3) π in³. One day, her sink clogged. She has to use one of two conical cups to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.

(a) One cup has a diameter of 4 in. and a height of 8 in. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.

(b) One cup has a diameter of 8 in. and a height of 8 in. How many cups of water must she scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.

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