## Calculus used to determine

Surface Area and Volume of Sphere

## Surface Area

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

= 2πr.2[-cosø]

= 2πr2[0 - (–1)]

= 2πr2

AREA OF SPHERE = 4πr2