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

A = 9π cm²

Step-by-step 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

1.0

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is