Uploaded June 2026 | Updated September 2026, 1 week ago

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In this lesson, you're going to learn how to find the volume of a sphere when a cube with a side length of 8 units is inscribed within it! This interesting geometry problem requires us to first find the diameter of the sphere, which is the space diagonal of the inscribed cube. We'll use the Pythagorean theorem and special right triangles to solve for the radius, and then calculate the sphere's volume.

Here's what we'll cover:

00:00 Introduction to Finding the Volume of an Inscribed Sphere
0:40 Understanding the Relationship Between an Inscribed Cube and Sphere
1:15 Step 1: Finding the Diagonal of the Cube's Base (using 45-45-90 triangles)
2:30 Step 2: Finding the Space Diagonal of the Cube (which is the sphere's diameter)
3:45 Step 3: Calculating the Radius of the Sphere
4:15 Step 4: Applying the Volume of a Sphere Formula (V = 4/3 * pi * r^3)
5:00 Step 5: Simplifying the Volume Calculation
By the end of this video, you'll be able to confidently solve problems involving inscribed cubes and spheres, applying key geometric principles!

#VolumeOfSphere #InscribedCube #Geometry #MathProblem #PythagoreanTheorem #SpecialRightTriangles

Learn More Here:
Volume of a Sphere
youtu.be/Ax1RQsxETIk

Special Right Triangles
youtu.be/Y_qs4cgxbgs

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