Calculus used to determine
Surface Area and Volume of Sphere
Consider circle centred on origin radius r.
General Point on circle is (r,ø).
Consider point on circle (r+∂r,ø+∂ø).
The arc between the 2 points is length r∂ø.
Rotate the arc about x-axis to create annulus.
If ∂ø is small the area of this annulus ≈ 2π.r.sinø.r∂ø. = 2πr2 sinø.∂ø
AREA OF HEMISPHERE = 2πr.2∫₀π´²sinø.dø
= 2πr2[0 - (–1)]
AREA OF SPHERE = 4πr2