Answer:
1. Not congruent
2. Not congruent
3. Congruent
4. Congruent
5. Not congruent
6. Not congruent
???
Step-by-step explanation:
The volume of a sphere is (4/3) (pi) (radius cubed).
The volume of one sphere divided by the volume of another one is
(4/3) (pi) (radius-A)³ / (4/3) (pi) (radius-B)³
Divide top and bottom by (4/3) (pi) and you have (radius-A)³ / (radius-B)³
and that's exactly the same as
( radius-A / radius-B ) cubed.
I went through all of that to show you that the ratio of the volumes of two spheres
is the cube of the ratio of their radii.
Earth radius = 6,371 km
Pluto radius = 1,161 km
Ratio of their radii = (6,371 km) / (1,161 km)
Ratio of their volumes = ( 6,371 / 1,161 ) cubed = about <u>165.2</u>
Note:
I don't like the language of the question where it asks "How many spheres...".
This seems to be asking how many solid cue balls the size of Pluto could be
packed into a shell the size of the Earth, and that's not a simple solution.
The solution I have here is simply the ratio of volumes ... how many Plutos
can fit into a hollow Earth if the Plutos are melted and poured into the shell.
That's a different question, and a lot easier than dealing with solid cue balls.
8.25 / 11 = 0.77 times 18 = 13.86 the answer would be 13.86
