3D Geometry
Sphere
Grade 12
Question:
<p>Radius of the sphere, with <span class="math">(2, -3, 4)</span> and <span class="math">(-5, 6, -7)</span> as extremities of a diameter, is</p>
<p>(a) \(\frac{251}{2}\)</p>
<p>(b) \(\frac{251}{3}\)</p>
<p>(c) \(\frac{\sqrt{251}}{4}\)</p>
<p>(d) \(\frac{\sqrt{251}}{5}\)</p>
Step-by-Step Solution
Key Concept: When two points are extremities of a diameter, the radius is half the distance between them.
Step 1: Distance between the two points is the diameter. Distance = \(\sqrt{(2-(-5))^2 + (-3-6)^2 + (4-(-7))^2} = \sqrt{49 + 81 + 121} = \sqrt{251}\) Step 2: Radius = Diameter/2 = \(\frac{\sqrt{251}}{2}\) ∴ Answer is (a).
Correct Answer: A