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.
Answer:
Okay So I see you need to change 1/3 to a denominator of 6
You don't do anything to the -1/6
But to change the 1/3 you need to multiply 3 and 1 by two, which is 2/6
And the -1/6 stays the same
The solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3
<h3>How to simplify algebraic equations?</h3>
We want to simplify the algebraic equation;
1000(7x - 10) = 50(292 + 100x)
The first step is to use distributive property of equality to expand the bracket to get;
7000x - 10000 = 14600 + 5000x
7000x - 5000x = 14600 + 10000
2000x = 24600
Use division property of equality to divide both sides by 2000 to get;
x = 24600/2000
x = 12.3
Thus, we can conclude that the solution to the given algebraic equation 1000(7x - 10) = 50(292 + 100x) is; x = 12.3
Read more about algebraic equations at; brainly.com/question/723406
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I can't answer this question without a picture of the lines.
Answer:
90 sq inches
Step-by-step explanation:
The lateral area is the side area of the pyramid. In this case, there are 3 sides because the base is a triangle. Since the base is an equilateral triangle, all sides are of equal dimensions. So, the sides of the pyramid are also all of the same size, area.
We then just have to figure out the area of one of the side triangles, then multiply it by 3 to get the total lateral area of that pyramid.
We know how to calculate the area of a triangle: A = (b * h)/2
In this case, b = 5 in, h = 12 in. So,
TA = (5 * 12)/2 = 60 / 2 = 30
Each side triangle has an area of 30 sq inches.
LA = 3 * TA (since there are 3 sides)
LA = 3 * 30 = 90 sq inches
