Question

if area of a circle varies directly as the cube of the radius, when the area is 625cm the radius is 5cm. calculate the area of a circle of radius 8​

Answer 1

2560 cm²

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 =
`(A)/(r^3)` =
`(625)/(5^3)` =
`(625)/(125)` = 5

A = 5r³ ← equation of variation

When r = 8, then

A = 5 × 8³ = 5 × 512 = 2560 cm²