QuestionJune 15, 2025

How can you tell where one sphere ends and the next one begins? You find the exact point where they meet. You calculate which sphere is more involved. There are no hard rules, and often spheres overlap. You look it up in a textbook.

How can you tell where one sphere ends and the next one begins? You find the exact point where they meet. You calculate which sphere is more involved. There are no hard rules, and often spheres overlap. You look it up in a textbook.
How can you tell where one sphere ends and the next one begins?
You find the exact point where they meet.
You calculate which sphere is more involved.
There are no hard rules, and often spheres
overlap.
You look it up in a textbook.

Solution
3.9(155 votes)

Answer

The exact point where they meet is determined by calculating the intersection based on distance and radii. Explanation 1. Identify the point of intersection Determine the exact point where two spheres meet by finding their intersection. 2. Calculate the distance between centers Use the formula for distance d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} to find the distance between the centers of the spheres. 3. Compare radii and distance If the sum of the radii equals the distance, they touch externally. If the difference of the radii equals the distance, they touch internally.

Explanation

1. Identify the point of intersection<br /> Determine the exact point where two spheres meet by finding their intersection.<br />2. Calculate the distance between centers<br /> Use the formula for distance $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$ to find the distance between the centers of the spheres.<br />3. Compare radii and distance<br /> If the sum of the radii equals the distance, they touch externally. If the difference of the radii equals the distance, they touch internally.
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