Answer:
2560 cm²
Step-by-step explanation:
Given that the area (A) varies directly as the cube of the radius (r) then the equation relating them is
A = kr³ ← k is the constant of variation
To find k use the condition A = 625 when r = 5
k = [tex]\frac{A}{r^3}[/tex] = [tex]\frac{625}{5^3}[/tex] = [tex]\frac{625}{125}[/tex] = 5
A = 5r³ ← equation of variation
When r = 8, then
A = 5 × 8³ = 5 × 512 = 2560 cm²
