7 Maximum distance on two spheres

TL;DR

The maximum possible length between two points on tangent spheres with radii of 7 and 4 is 22 units.

Transcript

• [Voiceover] Two spheres, one with radius seven, and one with radius seven, and one with radius four are tangent to each other. If P is any point on one sphere and Q is any point on the other sphere, what is the maximum possible length of PQ? So, let's think about this. So, let me draw the sphere with radius seven. And obviously the sphere is a th... Read More

Key Insights

• ❓ Two spheres with radii of 7 and 4 are tangent to each other.
• 😥 The maximum distance between any point on one sphere and any point on the other is 22 units.
• 🌥️ While the proof for this maximum distance may require more rigorous reasoning, it is evident from available choices that 22 is the largest distance.
• 😥 The location of the tangent points does not affect the maximum distance.
• 😥 Tangent spheres share a common point or a common tangent plane without intersecting.
• ✈️ Visualizing spheres as circles in a two-dimensional plane can help understand the concept.
• 😥 The maximum distance is found by placing the points as far away from each other as possible.

Questions & Answers

Q: What is the definition of two spheres being tangent to each other?

Two spheres are tangent to each other when they share a common point or a common tangent plane, meaning they touch each other without intersecting.

Q: How can we visualize the spheres in two dimensions?

While spheres are three-dimensional objects, we can represent them as circles in a two-dimensional plane to understand the concept better.

Q: Is the maximum distance between the points P and Q dependent on the locations of the tangent points?

No, the maximum distance between P and Q is not determined by the location of the tangent points. It solely depends on the radii of the spheres.

Q: Why is the distance between points P and Q on the two spheres equal to the sum of their diameters?

The distance between P and Q is equal to the sum of their diameters because the spheres are tangent to each other. Therefore, the distance between the tangent points is equal to the sum of their radii.

Summary & Key Takeaways

• Two spheres, one with a radius of 7 and the other with a radius of 4, are tangent to each other.

• The goal is to find the maximum distance between any point on one sphere and any point on the other.

• By placing the points as far away from each other as possible, the maximum distance is found to be 22 units.