An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available

Question

3 years ago

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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.
3 inches
4 inches
6 inches
8 inches
9 inches

Mathematics

2 answers:

Sergeu [11.5K] · Answer 1 · 2022-09-16T22:25:05+03:00

Since all the volume of the liquid will be contained by all 30 spheres then,
30 V = 3392.92

where V is the volume of each sphere
Solving for V
V = 113.0973

The formula for the volume of the sphere is:
V = (4/3) π r³

Since diameter, D = 2r
V = (4/3) π (D/2)³
V = (4/3) π (1/8) D³
V = (1/6) π D³

Since V = 113.0937
113.0937 = (1/6) π D³
D = 6

<span>Therefore, the diameter is 6 inches </span>

Igoryamba · Answer 2 · 2022-09-17T00:10:19+03:00

To find out how much is poured into each sphere divide 3 392.92 by 30 which is 113.097. This is the volume in each individual sphere.
The volume of a sphere is calculated using the formula 4/3 x pie x r^3. From here you could either substitute your possible answers into the equation (Remembering to divide by 2 because your answers are the diameters) or you could work backwards and multiply by 2 at the end.
Hope this helps