Mathematics: Acylindrical 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. what is the volume of water in the vase?

The answer is 7x - 3Step-by-step explanation:...

Acylindrical vase has a diameter of 6 inches. at

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harry5112

30.05.2020

Mathematics

$V_{vase-marble}=\frac{135}{2}\pi \:in^{3} \:or\: V_{vase-marbles}\approx 212.06 \:in^{3}$

Step-by-step explanation:

1) Each marble is a sphere whose volume is given by this formula:

$V_{sphere}=\frac{4}{3}\pi r^{3}$

2) There are 9 marbles at the bottom whose radius is 1.5 inches:

$V_{sphere}=\frac{4}{3}\pi r^{3}\Rightarrow V_{sphere}=\frac{4}{3}\pi*(1.5)^{3} \Rightarrow V=\frac{9}{2}\pi$

$V_{9 marbles}=9*\left ( \frac{9}{2}\pi \right )\Rightarrow V=\frac{81}{2}\pi \approx400 \:in^{3}$

3) The volume of this vase with Marbles. Since the mark is on the 12 then we have to plug for the height 12 inches. And Subtract the Volume of the Vase without the marbles less the volume with the 9 marbles at the bottom.

$V_{vase-marbles}=\pi*r^{2}*h\Rightarrow V_{vase-marbles}=\pi*(3)^{2}*(12)-(\frac{81}{2})\pi\Rightarrow V_{vase-marbles}=108\pi-(\frac{81}{2})\pi=\frac{135}{2}\pi \:in^{3} \Rightarrow V_{vase-marbles}\approx 212.06 \:in^3$

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Acylindrical 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. what is the volume of water in the vase?

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