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sergejj [24]
3 years ago
14

the circumference of the great circle of a sphere is 12 pi inches. Which of the following expressions can be used to approximate

the volume of the sphere?

Mathematics
1 answer:
andriy [413]3 years ago
4 0
It would be A because with volume you would have your 12 to the 3rd power then multiply it by pie which is 3.14 then for sphere you would then multiply what ever you got after multiplying 12 to the 3rd power then by 3.14 to the 4/3
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Answer:

125/216 or (5/6)³

Step-by-step explanation:

height of water column=5/6 ×12=10 cm

radius of water level=10/12×6=5 cm

volume of water=π ×5²×10=250 π cm³

volume of cone=π×6²×12=432 π cm³

reqd. ratio=250 π/432 π=125/216=(5/6)³

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Answers:

  1. Plane EFGH
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==================================================

Explanation:

Problem 1

The plane ABCD is the floor of the box or room.

The ceiling plane EFGH is parallel to the floor.

Parallel planes never intersect, must like how parallel lines in 2D never intersect. As such, parallel planes are the same distance apart.

In contrast, something like plane ABFE intersects with ABCD along the segment AB. This shows ABFE is not parallel to ABCD.

----------------------

Problem 2

Same side interior angles, aka consecutive interior angles, are inside the parallel (or nearly parallel) lines. One such example is angle 2 and angle 3. The other pair being angle 6 and angle 7. They must be on the same side of the transversal.

In contrast, alternate interior angles would be something like the pair angle 2 and angle 7. The other pair being angle 3 and angle 6. This time the angles are on alternating or opposite sides of the transversal.

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Problem 3

Angles 1 and 8 are exterior of the parallel (or nearly parallel) lines. They are on alternating sides of the transversal. Therefore, we consider them to be alternate exterior angles.

----------------------

Problem 4

The use of "alternate" refers to the idea the angles are on opposite or alternating sides of the transversal line. The transversal line is the line that crosses the two other lines that are almost parallel.

I like to think of the parallel (or nearly parallel) lines as train tracks. The transversal is the roadway that crosses both train tracks. Then we could have locations 1 and 8 on opposite sides of the roadways to represent the alternate exterior angles.

As you can probably guess or know by now, the "exterior" is from the angles being outside or exterior of the parallel (or nearly parallel) lines.

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