Question

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of 4000/3*π in^3. 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. Hint: you may need to find the volume for both.
(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, and make certain to show your work.

(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, and make certain to show your work.

Answer 1

Answer:

  (A)  125 scoops

  (B)  31 scoops

Step-by-step explanation:

The volume of a cup in terms of radius and height is ...

  V = (1/3)πr²h

The radius is half the diameter, so the volume in terms of diameter is ...

  V = (1/3)π(d/2)²h = (π/12)d²h

The number of cups it takes to empty the sink will be the sink volume divided by the cup volume, so will be ...

  n = (4000π/3)/((π/12)d²h)

  n = 16000/(d²h)

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(A) The number of cups required of diameter 4 and height 8 is ...

  n = 16000/(4²·8) = 125

  125 scoops are required to empty the sink

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(B) The number of cups required of diameter 8 and height 8 is ...

  n = 16000/(8²·8) = 31.25 ≈ 31

  31 scoops are required to empty the sink