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A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches.
Which of the following could be used to calculate the volume of water in the vase?

π(3in)2(12in) − 1.5(four over threeπ(9in)3)
π(12in)2(3in) − 1.5(four over threeπ(9in)3)
π(3in)2(12in) − 9(four over threeπ(1.5in)3)
π(12in)2(3in) − 9(four over threeπ(1.5in)3)

Respuesta :

mhanifa

Answer:

  • C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)

Step-by-step explanation:

Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.

Volume of cylinder up to water level:

  • Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)

Volume of marbles:

  • Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)

Volume of water:

  • Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)

Correct choice is C

VERIFIEDNOT

Answer:

C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)

Step-by-step explanation:

  • Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.

  • Volume of cylinder up to water level:

Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)

  • Volume of marbles:

Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)

  • Volume of water:

Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)

Correct choice is C

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