Question

The area of a circle varies directly with the square of its radius.if the area 4πcm² when the radius is 2cm, find the area when the radius is 3cm

Answer 1

A = 9π cm²

Explanation:

Given that area (A) varies directly with r² then the equation relating them is

A = kr² ← k is the constant of variation

To find k use the condition A = 4π when r = 2 , then

4π = k × 2² = 4k ( divide both sides by 4 )

π = k

A = πr² ← equation

when r = 3 , then

A = π × 3² = 9π cm²