# 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.

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 $a^{2}$ —- —- Rectangle 2(w+h) w.h —- —- Parallelogram 2(a+b) b.h —- —- Trapezoid a+b+c+d $\frac{1}{2}(a+b)\times h$ —- —- 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) $2 h(l+b)$ $l \times b \times h$ Cube 6a $6a^{2}$ $4a^{2}$ $a^{3}$ 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 —- $3 \pi r^{2}$ $2 \pi r^{2}$ $\frac{2}{3}\pi r^{3}$

#### Practise This Question

In theΔABC given in the figure below, if DE divides AB and AC in the same proportion, then: