Ask Question
20 May, 18:34

Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of (2000/3) π in³. 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.

(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.

+2
Answers (1)
  1. 20 May, 18:37
    0
    Step-by-step explanation:

    The volume of the sink is (2000/3) π in³.

    The cups that she used in scooping water from the sink are conical. The formula for determining the volume of a cone is expressed as

    Volume = 1/3 * πr²h

    Where

    r represents the radius of the cone.

    h represents the vertical height of the cone.

    π is a constant whose value is 3.14

    From the information given,

    a) considering the first cup,

    Diameter of cup = 4 inches

    Radius = diameter/2 = 4/2 = 2 inches

    Height = 8 inches

    Therefore,

    Volume of cup = 1/3 * π * 2² * 8

    Volume = 1/3 * π * 4 * 8

    Volume = 32π/3 inches³

    The number of cups needed is

    2000π/3 : 32π/3

    = 2000π/3 * 3/32π

    = 2000/32 = 62.5

    Approximately 63 cups

    b) considering the second cup,

    Diameter of cup = 8 inches

    Radius = diameter/2 = 8/2 = 4

    Height = 8 inches

    Therefore,

    Volume of cup = 1/3 * π * 4² * 8

    Volume = 1/3 * π * 16 * 8

    Volume = 128π/3

    The number of cups needed is

    2000π/3 : 128π/3

    = 2000π/3 * 3/128π

    = 2000/128 = 15.625

    Approximately 16 cups
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Carissa also has a sink that is shaped like a half-sphere. The sink has a volume of (2000/3) π in³. One day, her sink clogged. She has to ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers