Geometry Notes: Circles, Polygons, and Volume Formulas

Equation of a Circle - Standard Form

(x−h)²+(y−k)²=r², where (h,k) is the center and r is the radius.

Diameter

Double the radius (2r).

Regular Polygon

A polygon with all sides and angles equal.

Sum of Interior Angles of a Polygon

(n−2)×180°, where n is the number of sides.

Sum of Exterior Angles of a Polygon

Always equals 360° for any polygon.

Area of a Triangle

A=1/2×Base×Height.

Surface Area of a Cube

SA=6a², where a is the length of a side.

Volume of a Cube

V=a³, where a is the length of a side.

Surface Area of a Rectangular Prism

SA=2lw + 2lh + 2wh, where l, w, and h are length, width, and height.

Volume of a Rectangular Prism

V=l×w×h.

Surface Area of a Sphere

SA=4πr², where r is the radius.

Volume of a Sphere

V=(4/3)πr³.

Surface Area of a Pyramid

SA=B+1/2Pl, where B is base area, P is perimeter, l is slant height.

Volume of a Pyramid

V=(1/3)Bh, where B is base area and h is height.

Surface Area of a Right Circular Cone

SA=πr² + πrl.

Volume of a Right Circular Cone

V=(1/3)πr²h.

Surface Area of a Cylinder

SA=2πr² + 2πrh.

Volume of a Prism

V=Bh, where B is the area of the base and h is the height.

Radius

Distance from the center to the edge of a circle or sphere.

Height

Perpendicular distance between the bases or the top and bottom of a solid figure.

Slant Height

Diagonal distance from the apex to the edge of a base in a cone or pyramid.

Base Area

Area of the base of a solid.