A cardioid has a radius a of 6
Calculate the area and polar equations
Cardioid Area (A) formula
A = 6πa2
Plug in a = 6
A = 6π62
A = 6π(36)
A = 216π or 678.5840131754
Cardioid Arc Length (L) Formula
L = 16a
Plug in a = 6
L = 16(6)
L = 96
Polar equation of horizontal cardioid
r = a(1 ± cos(θ))
r = 6(1 ± cos(θ))
Polar equation of vertical cardioid
r = a(1 ± sin(θ))
r = 6(1 ± sin(θ))
Final Answers:
A = 216π or 678.5840131754
L = 96
r = 6(1 ± cos(θ))
r = 6(1 ± sin(θ))
L = 96
r = 6(1 ± cos(θ))
r = 6(1 ± sin(θ))
What is the Answer?
A = 216π or 678.5840131754
L = 96
r = 6(1 ± cos(θ))
r = 6(1 ± sin(θ))
L = 96
r = 6(1 ± cos(θ))
r = 6(1 ± sin(θ))
How does the Cardioid Calculator work?
Free Cardioid Calculator - Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid
This calculator has 1 input.
This calculator has 1 input.
What 4 formulas are used for the Cardioid Calculator?
A = 6πa2
L = 16a
r = a(1 ± cos(θ))
r = a(1 ± sin(θ))
L = 16a
r = a(1 ± cos(θ))
r = a(1 ± sin(θ))
What 4 concepts are covered in the Cardioid Calculator?
- arc
- a portion of the boundary of a circle or a curve
- area
- Number of square units covering the shape
- cardioid
- a heart-shaped curve. a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius.
- polar equation
- any equation that describes a relation between r and θ
