2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of. 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.

Question

Cameron Schaefer

Mathematics

10 September, 05:32

2. Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of. 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.

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Jack Galloway · Answer 1

(a) Volume of 1st cup = (1/3) pi * (4/2) ^2 * 8 = 32/3 pi in^3

# scoops = (2000/3) pi / (32/3) pi = 2000/32 = 62.5 ≈ 63

(b) Volume of 2nd cup = (1/3) pi * (8/2) ^2 * 8 = 128/3 pi in^3

# scoops = (2000/3) pi / (128/3) pi = 2000/128 = 15.625 ≈ 16