# Surface Areas & Volumes

Surface Areas & Volumes - Complete Collection#### Summary

###### Class 9 Maths: Surface Areas & Volumes - Complete Collection

#### Overview

Area is the amount of space inside a boundary of a 2D object.

**Surface area** of a solid 3D object is the measure of the total area that a surface of an object occupies. It is measured in m^{2}, cm^{2} etc

We generally talk about inner surface area & outer surface area.

Surface area is typically used to determine cost of painting for a given 3D object.

**Volume** is the quantity of 3D space enclosed by some closed boundary. It is measured in m^{3}, cm^{3}, ltr etc.

It is typically used to determine quantity of liquid, air, grains etc in a 3D container.

We will study Surface Area & Volume for Cube, Cuboid, Sphere, Cone and Cylinder.

Let’s define these terms

**Cuboid**: Box shaped 3D solid object with 6 flat sides. All angles are right angles & all faces are rectangle.**Cube**: Box shaped 3D solid objects with 6 flat side. All angles are right angles & all faces are square. All sides are equal.**Sphere**: Perfectly round geometrical & circular 3D object like a ball. It is set of all points that are all at same distance from a given point (center) in a 3D space.**Hemisphere**: It is half of sphere.**Cylinder**: 3D surface formed by the points at a fixed distance from a given line segment called Axis. Solid enclosed by this surface & 2 planes perpendicular to axis is called cylinder.**Right Circular Cylinder:**Cylinder where 2 planes are circular & also these planes are perpendicular to axis.**Cone**: 3D object that tapers smoothly from a flat base to a point called apex or vertex. Base need not be circular**Right Circular Cone**: Cone with circular base & also base perpendicular to axis.

It has huge application in day to day life.

- Surface Area is used to find cost of painting a wall
- Volume is Used to find cost of building a wall
- Surface Area is used find cost of creating a box
- Volume is used to find the weight of grains that a box can hold
- Volume can also be used to find number of people that can stand in a room
- Surface area concept is required to find the cloth required to build a tent
- Surface area concept is also used to find cost of making pencil stand
- Volume Concept can be used to find number of pencils that a pencil stand can hold
- Volume concept can also be used to find the volume of water in a tank or well

2D sheets can be piled together to form 3D Cuboid

2D circular plates can be piled to form 3D Cylinder

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