1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 2000/3 pi in3. One day, his sink clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Anthony begins scooping.

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

Question

Mathematics

Duckling

7 September, 09:05

1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 2000/3 pi in3. One day, his sink clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Anthony begins scooping.

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

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Answers (1)

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Tiffany Mathis · Answer 1

Volume of a half sphere = (2 / 3) π r³

Volume of a cylinder = π r² h

Given:

V of sink = 2000/3 pi in³ →

2 cylindrical cups:

1) diameter: 4 in; height: 8 in.

2) diameter: 8 in; height 8 in.

V of cylinder 1 = π * 2² * 8 = π 32 in³

2000/3 / 32 = 2000/3 * 1/32 = 2000 / 96 = 20.83 or 21 cups

V of cylinder 2 = π * 4² * 8 = π 128 in³

2000/3 / 128 = 2000/3 * 1/128 = 2000 / 384 = 5.21 or 5 cups