An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

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14-06-2015
Mathematics

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An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

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naǫ naǫ · Answer 1 · 2015-06-18T16:26:06+02:00

The volume of a sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
r - the radius

3392.92 cubic inches are poured into 30 spheres.
[tex]3392.92=30 \times \frac{4}{3} \pi r^3 \\ \\ 3392.92=40\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ |\div 40 \\ \\ 84.823=\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div \pi \\ \\ r^3=\frac{84.823}{\pi} \\ \\ r=\sqrt[3]{\frac{84.823}{\pi}} \\ \\ r \approx \sqrt[3]{27} \\ \\ r \approx 3[/tex]

The diameter is twice the radius.
The diameter of each sphere should be approximately 6 inches.

dorianpadilla22 dorianpadilla22 · Answer 2 · 2020-05-12T19:37:14+02:00

dorianpadilla22 dorianpadilla22

12-05-2020

Answer:

6 inches

Step-by-step explanation:

correct on Plato/ edmentum courseware

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