Question

a circle has a diameter of 14 ft. if the area is tripled what happens to the circumference.

Answer 1

Diameter of the circle (d ) = 14ft.

Radius (r 1) = d / 2 = 7ft.

Area of the circle (A 1) = πr ^2.

Substitute the value of r 1 = 7 in A 1 = πr ^2.

A 1 = π * 7^2

A 1 = π * 49.

The area is tripled, means that,

A 2 = 3A 1 = 3 * π * 49

πr 2^2 = 3 * π * 49

r 2^2  = 3 * 49 = 147

r 2 = sqrt (147) = 12.12ft.

Circumference 1 = 2 *  π * r 1 = 2 *  π * 7 = 14π .

Circumference 2 = 2 *  π * r 2 = 2 *  π * 12.12 = 24.24π .

Increased circumference = 24.24π  / 14π = 1.731.

Therefore, the circumference will increase by 1.731 ft.

Answer 2

The diameter of the circle is 14 ft.

Here the area is tripled, so A₂ = 3A₁.

The relation between radius(r) and area(A) is r₁/r₂ = √(A₁/A₂).

The relation between circumference(C) and radius(r) is C₁/C₂ =  r₁/r₂.

Therefore relation between circumference(C) and radius(r) and area(A) is

C₁/C₂ =  r₁/r₂ = √(A₁/A₂).

C₁/C₂ =  √(A₁/A₂).

C₁/C₂ =  √(A₁/3A₁).

C₁/C₂ =  √(1/3).

C₂ =  √3C₁.

The circumference will increased by √3 = 1.731.