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You will need to use the small cup 9 times or the larger cup 2 times.
The volume of the sink is 700 in^3
The smaller cup is a cylinder with a diameter of 4 in and a height of 8 in, its volume is:
V = 3.14*(4in/2)^2*8in = 100.48 in^3
To remove all the water in the sink you will need:
N = 700 in^3/100.48 in^3 = 6.97 = 7
You will need to scoop the water 7 times.
For the larger cup, the diameter of 8 in and a height of 8 in, its volume is:
V' = 3.14*(8in/2)^2*8in = 401.92 in^3
You will need to scoop the water:
N' = 700 in^3/401.92 in^3 = 2 times.
If you want to learn more about volumes, you can read:
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