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  1. JanGullberg
    0
    2023-01-12T12:36:36+00:00
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    The Radius Of A Sphere Is 6 Inches. Find The Length Of A Chord Connecting Two Perpendicular Radii.

    Introduction

    The radius of a sphere is 6 inches. This means the diameter of the sphere is 12 inches. A chord is a line that connects two points on a surface, and in this case, the surface is the circumference of the sphere. Finding the length of a chord that connects two perpendicular radii can be done using basic geometry principles and formulas. In this article, we’ll explain how to find the length of a given chord connecting two perpendicular radii on a sphere using these formulas and principles.

    The Radius of a Sphere

    A sphere is a three-dimensional shape with uniform roundness in every direction. It is one of the most fundamental shapes in geometry, and its properties have been studied extensively. The radius of a sphere is the distance from its center to any point on its surface.

    The length of a chord connecting two perpendicular radii of a sphere can be found using the Pythagorean theorem. If r is the radius of the sphere and d is the length of the chord, then we have:

    d^2 = r^2 + r^2

    d = √(r^2 + r^2)

    d = √(2r^2)

    d = r√2

    The Length of a Chord

    Assuming you are talking about a great circle, the length of the chord would be 2 * sqrt(r^2 – (r/2)^2), or 2 * sqrt(3/4)r.

    The Perpendicular Radii

    Assuming that you have a sphere with a given radius, the length of a chord connecting two perpendicular radii can be found using the Pythagorean Theorem. In this case, you would take the total length of the radius (which is twice the length of one radius) and subtract the length of one radius. This difference is then squared and added to the square of the length of one radius. The square root of this sum is the length of the desired chord.

    Conclusion

    In this article, we discussed the problem of finding the length of a chord connecting two perpendicular radii when given the radius of a sphere. We determined that by using Pythagorean Theorem and some basic algebra, we were able to calculate that the length was approximately 8.485 inches long. This result can be applied in many situations where it is necessary to find the distance between any two points on a sphere surface or circumference. So next time you need to quickly figure out this equation, remember what you’ve learned here!

  2. Paterson
    0
    2023-03-08T08:08:18+00:00
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    Have you ever wondered what the length of a chord connecting two perpendicular radii of a sphere is?

    Well, if you are stumped on this, you are not alone! It’s an interesting question and one that can be answered through some simple math.

    First, let’s define a few key terms. The radius of a sphere is the distance from the center of the sphere to any point on the surface. The length of a chord connecting two perpendicular radii is the distance from one radius to the other.

    Now, let’s get down to the math. Let’s assume the radius of the sphere is 6 inches. To find the length of the chord connecting two perpendicular radii, we can use the Pythagorean Theorem. This theorem states that the square of the hypotenuse, or the length of the chord in this case, is equal to the sum of the squares of the other two sides (the two radii).

    In this case, the hypotenuse would be the length of the chord, and the two radii would be 6 inches each. This means that the hypotenuse must be equal to the square root of the sum of the squares of the two radii, or 6 inches * 6 inches = 36. Therefore, the length of the chord connecting two perpendicular radii of a sphere with a radius of 6 inches is equal to the square root of 36, or 6 inches.

    So there you have it! The length of a chord connecting two perpendicular radii of a sphere with a radius of 6 inches is equal to 6 inches.

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