Honors Geometry Chapter 12: Areas and Volumes of Solids

Total Area (T.A.)

area of ALL solid faces

Lateral Area (L.A.)

area of ALL lateral surfaces

2b

area of BOTH bases

Formula for the Lateral Area of a right prism

(perimeter)(height)

Formula for the Lateral Area of a pyramid

½perimeter(slant height)

Formula for the Surface Area of a pyramid

½perimeter(slant height) + base

Formula for the Volume of a pyramid

⅓hb

Formula for the Lateral Area of a cylinder

2πrh

Formula for the Total Area of a cylinder

2πrh + 2πr^2

Formula for the Lateral Area of a cone

πr(slant height)

Formula for the Total Area of a cone

πr(slant height) + πr^2

Formula for the Volume of a cone

⅓πr^2

Formula for the Surface Area of a sphere

4πr^2

Formula for the Volume of a sphere

4/3πr^3

If the scale factor of two similar solids is a : b, the…

• ratio of the corresponding perimeter stays the same

• ratio of the base areas, lateral areas, and total areas is squared

• ratio of the volumes is cubed