Question

find the area of a circle with diameter=40cm​

Answer 1

Answer: A = πr2 = π(d

2

)2 A = C2

4π

π = 3.1415

A = area

C = circumference or perimeter

r = radius, d = diameter

Solution Steps:

Area of a circle in terms of radius:

Area = π·r2 = 3.14·202 = 1257 square cm(*)

Area of a circle in terms of diameter:

Area = π·(d

2

)2 = 3.14·(40

2

)2 = 3.14·(20)2 = 1257 square cm(*)

Area of a circle in terms of circumference:

Area = C2

4π

= 125.72

4π

= 15800.49

(4·3.14)

= 15800.49

12.56

= 1257 square cm(*)

(*) 1256.6370614359 cm, exactly or limited to the precision of this calculator (13 decimal places).

Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.

Result in other units of area:

A circle of radius = 20 or diameter = 40 or circumference = 125.7 cm has an area of:

1.257E-7 square kilometers (km²)

0.1257 square meters (m²)

1257 square centimeters (cm²)

125700 square millimeters (mm²)

4.8533 × 10-8 square miles (mi²)

0.150336 square yards (yd²)

1.35302 square feet (ft²)

194.835 square inches (in²)

 

 

Use the this circle area calculator below to find the area of a circle given its diameter, or other parameters. To calculate the area, you just need to enter a positive numeric value in one of the 3 fields of the calculator. You can also see at the bottom of the calculator, the step-by-step solution.

Formula for area of a circle

Here a three ways to find the area of a circle (formulas):

Circle area formula in terms of radius

A = πr2  

Circle area formula in terms of diameter

A = π(d

2

)2

Circle area formula in terms of circumference

A = C2

4π

See below some definitions related to the formulas:

Circumference

Circumference is the linear distance around the circle edge.

Radius

The radius of a circle is any of the line segments from its center to its perimeter. The radius is half the diameter or r = d

2

.

Diameter

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is twice the radius or d = 2·r.

The Greek letter π