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

 Apr 10, 2023
 #1
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(a) 14 cups

 

(b) 38 cups

 Apr 10, 2023
 #2
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Volume of a cylinder:
V = π a^2 h    [a = radius] and [h=height]

 

 

1 - Pi x 4/2 x 8 =50.265 in^3 - volume of the first cup

2000/3 * Pi=2,094.395 in^3 - volume of water in the sink

2,094.395 / 50.265 =41.667 =42 scoops to empty the sink using first cup.

 

2 - Follow exactly the same procedure for the 2nd cup. 

 Apr 10, 2023
 #3
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1 - Pi x 2^2 x 8 ==100.531 cubic inches - volume of the first cup

2000/3 * Pi ==2094.395 cubic inches - volumes of water in the sink.

2094.395 / 100.531 ==20.833 ==21 - scoops to empty the water in the sink.

 

Note: Guest #2 forgot to square the radius of the cup.

Guest Apr 10, 2023

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