Geometry: Volume and Surface Area Formulas

Flashcards based on lecture notes covering surface area and volume formulas for various three-dimensional geometric solids.

Total Area (Prism or Cylinder)

$$2B + LA$$

Lateral Area (Prism)

$$P_{base} \times h$$

Lateral Area (Cylinder)

2\text{\pi}rh

Total Area (Cone)

$B + LA$ or \text{\pi}r^2 + \text{\pi}rl

Slant height ($l$)

Represented as the hypotenuse of the right triangle formed inside the solid.

Surface Area (Sphere)

4\text{\pi}r^2

Volume (Prism or Cylinder)

$$B \times h$$

Volume (Cylinder)

\text{\pi}r^2h

Surface Area (Hemisphere with base)

3\text{\pi}r^2

Surface Area (Hemisphere without base)

2\text{\pi}r^2

Volume (Cone or Pyramid)

$$\frac{1}{3} B \times h$$

Volume (Sphere)

\frac{4}{3} \text{\pi}r^3

Volume (Hemisphere)

\frac{2}{3} \text{\pi}r^3

Total Area (Pyramid)

$$B + LA$$

Lateral Area (Pyramid)

$$\frac{1}{2} \times P_{base} \times l$$

$B$ (in Volume and Surface Area formulas)

Area of Base

$$LA$$

Lateral Area