1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 2000/3π 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.

Question

Mathematics

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11 June, 22:42

1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 2000/3π 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.

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Answers (1)

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Jean Porter · Answer 1

The volume of the sink shaped like a half sphere is [2000/3] π in^2.

a) The volume of a cylinder is the area of the base * height

For this part the cup has a diameter, d, of 4 in and height, h, of 8 in.

The area of the base is π (d/2) ^2 = π (2 in) ^2 = 4π in^2.

The volume of the cuo is 4π in^2 * 8 in = 32π in^3.

Then the number of cups to take the volume of [2000 / 3] π in^2 is:

[2000 / 3]π / [32π] = 20.83

Answer: 21 cups.

b) For this part the diameter of the cup is 8 in and the height is 8 in

Then the volume is π (4 in) ^2 * 8 in = 128 ⇅ in^3

And the number of cups needed is [2000π/3] / (128π) = 5.2

Answer: 5 cups