A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 8 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 10 inches. Which of the following could be used to calculate the volume of water in the vase?

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A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 8 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 10 inches. Which of the following could be used to calculate the volume of water in the vase?

Mathematics
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Oh! oops. π(10in)2(3in) − 1.5(four over threeπ(8in)3) π(3in)2(10in) − 1.5(four over threeπ(8in)3) π(10in)2(3in) − 8(four over threeπ(1.5in)3) π(3in)2(10in) − 8(four over threeπ(1.5in)3)
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Using the height of the water as the height of a cylinder, what is the volume of water if there were no marbles in the cylinder?
okay wait im confused
Let's find the volume of water you can fit in the vase if there are no marbles in it. The vase is a cylinder of diameter 6 inches and height 10 inches. Can you calculate the volume of such a cylinder?
282.74
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Correct. Now by putting 10 marbles in the vase, the vase will not be able to hold as much water. The amount of water volume that will be reduced is the same as the combined volume of all the marbles. Each marble is a sphere. What is the volume of a sphere with diameter 3 inches?
14.14
Good. That is 1 marble. There are 8 of them. What is the volume of the 8 marbles?
113.12
Right. Now you subtract 282.74 - 113.12 all in in^3.
169.62 ?
Correct. In your choices you don't see numbers, you see expressions. Which expression in the choices shows what you just did? volume of cylinder - volume of 8 marbles?
|dw:1438032915804:dw|
c?
|dw:1438032948978:dw|
Oh okay so D?
Look carefully. In choice c., 10 in is squared in the cylinder formula. In the problem, 10 in. is the height. It is the 3 in. radius that is squared.
Correct. D is the answer. Good job!
Wow thank you so much!!!
You're welcome.

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