I need help remembering this.

Question

Consider the interior of an imaginary sphere on which the light shines. The surface area of the sphere is directly proportional to the square of the radius. If the surface area of a sphere with a 4-m radius is 64π^2, determine the exact surface area of a sphere with a 8-m radius.

Answer 1

Surface area and cross-sectional area vary with the square of the radius. So for 2 cases, you can say

(A₂/A₁ )= (r₂/r₁)² ie. you t3 x r --> you 3² or 9 times A (in terms of multipliers)

For solving a variation problem, you can rewrite the equation as

A₂ = A₁(r₂/r₁)² (which is just A₂ (A₂/A₁) = A₂)

case 1 is 64π cm² = A (no π²) and r₁ = 4 cm

case 2 has r₂ = 8 cm find A₂