# Surface Areas and Volume

## Area

The space occupied by a two-dimensional flat surface. It is measure in square units.

Generally, Area can be of two types

(i) Total Surface Area

(ii) Curved Surface Area

### Total surface area

Total surface area refers to area including the base(s) and the curved part.

### Curved surface area (lateral surface area)

Refers to area of only the curved part excluding it’s base(s).

### Volume

The amount of space, measured in cubic units, that an object or substance occupies. Some shapes are two-dimensional, so it doesn’t have volumes. Example, Volume of Circle cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

Below given is the table for calculating Surface area and Volume for the basic geometrical figures:

 Name Perimeter Total Surface Area Curved Surface Area Volume Figure Square 4a a2 —- —- Rectangle 2(w+h) w.h —- —- Parallelogram 2(a+b) b.h —- —- Trapezoid a+b+c+d 1/2(a+b).h —- —- Circle $2 \pi r$ $\pi r^{2}$ —- —- Ellipse $2\pi\sqrt{\left ( \frac{a^{2}+b^{2}}{2} \right )}$ $\pi a.b$ —- —- Triangle a+b+c $\frac{1}{2}\times b \times h$ —- —- Cuboid 4(l+b+h) 2(lb+bh+hl) 2h(l+b) $l \times b \times h$ Cube 6a 6a2 4a2 $a^{3}$ Cylinder —- $\pi r(r+h)$ $2 \pi r h$ $\pi r^{2} h$ Cone —- $\pi r(r+l)$ $\pi r l$ $\frac{1}{3}\pi r^{2} h$ Sphere —- $4 \pi r^{2}$ $4 \pi r^{2}$ $\frac{4}{3}\pi r^{3}$ Hemisphere —- $3 \pi r^{2}$ $2 \pi r^{2}$ $\frac{2}{3}\pi r^{3}$