Question

Discuss a more accurate method for approximating the volume of the spherical slab other than using just cylindrical slabs. Discuss in two to three sentences.

Answer 1

Answer:

The volume of the a sphere can be approximated by the rotation of a circle

Step-by-step explanation:

The volume of a sphere can be found by rotating a circle which is the cross section of the sphere about the x axis that is rotating x² + y² = a²

In the process of rotation, each cross section of the sphere generated will have a radius y from which the area of that cross section is π·y² = π·(a² - x²)

Therefore, integrating from +a to -a gives the volume of the sphere as π×[a³ - x³/3]ᵃ₋ₐ which is equal to 4/3·π·r³ (the exact volume of a sphere).