Geometry Chapter 11: Circumference, Area, and Volume

Formula for Circumference

C=πd, where d is the diameter

or

C=2πr, where r is the radius

Formula for Arc Length

arc length of AB/2πr = mAB/360

Converting Degrees to Radians

2πradians/360
or
πradians/180

Converting Radians to Degrees

360/2πradians

or

180/πradians

Area of a Circle Formula

A=πr², where r is the radius of the circle.

Area of a Sector Formula

Area of Sector APB/ πr² = mAB/360

Area of a Rhombus or Kite Formula

A=½d₁d₂

where d₁ and d₂ are the diagonals.

Area of a Regular Polygon Formula

½ (apothem)(perimeter)

or

½ (apothem)(number of sides)

Volume of a Prism Formula

V=Bh

where B is the area of the base and h is the vertical height.

Volume of a Cylinder Formula

V=πr²h

where r is the radius of the circle base and h is the vertical height.

Volume of a Pyramid

V=1/3Bh

where B is the area of the base and h is the vertical height.

Surface Area of a Right Cone Formula

S=πr²+πrl

where r is the radius of the circle's base and l is the slant height.

Volume of a Cone Formula

V=1/3Bh

=1/3πr²h

where h is the vertical height and r is the radius of the base.

Surface Area of a Sphere Formula

S=4πr², where r is the radius.

Volume of a Sphere Formula

V=4/3πr³, where r is the radius.