# GRE Geometry | Three – Dimensional Figures

• Last Updated : 20 Jan, 2022

An object which has only height and length are called 2-dimensional figures while an abject which has height length and width are called 3-dimensional object.

Examples of 2-D figures:

Examples of 3-dimensional figures:

1. Cube: 1. In a cube length breadth and height are all equal.

`length = breadth = height `
1. let’s length, breadth and height as a.
It has 6 square face each with side length a.

```Volume of cube = a * a * a
Volume of cube = a3

Surface area of cube = 6 * area of one face
Surface area of cube = 6 * a2 ```
1.
2. Cuboid: 1. In a cuboid length breadth and height are not equal.
It has 6 square face,

```Volume of cuboid = length * breadth * height

Surface area of cuboid = 6 * area of one face
Surface area of cuboid = length * breadth
+ length * height
+ length * height

Surface area of cuboid = 2(length * breadth
+ length * height ) ```
1.
2. Sphere: 1. A sphere has radius, volume and surface area:

```Volume of sphere = (4 / 3) * π * radius * radius * radius
Volume of sphere = (4 / 3) * π * r3

Surface area of sphere = 4 * &pi * radius * radius
Surface area of sphere = 4 * &pi * radius2

Surface area of sphere = 2 * &pi * radius * radius ```
1.
2. Cylinder: 1. A cylinder is a solid or hollow circular shape object with two circular base.

```Volume of cylinder = π * radius * radius * h
Curved surface area of cylinder = 2 * π * radius * h
Total surface area = 2 * π * radius * h + 2 * &pi * radius * radius ```
1.
2. Cone: 1. A cylinder is a solid or hollow with one circular base and which tappers from base to a point.

```Volume of a cone  = (1 / 3)π * radius * radius * height

Curved surface area of a cone
= π * radius * slant height

Total surface area of cone
= π * radius * slant height
1.
2. Pyramid: 1. Pyramid is 3-d object with polygon base, this polygon base is connected to an apex in pyramid.

```Volume of a pyramid
= (area of base * height) / 3 ```
1.

Examples:

1. What will be the curved surface area of a cylinder having radius 5cm and height 10cm?

```Curved surface area of a cylinder
= 2 * π * r * height
= 2 * 22 / 7 * 5 * 10
= 314.285714286 cm2 ```
1.
2. What will be the slant height of a cone which have curved surface area 990 cm2 and radius 5 cm?

```Curved surface area of a cone = π * radius * slant height
π * radius * slant height  = (22 / 7) * 5 * l
l = 63cm ```
1.
2. What is the volume of a square base pyramid having base side 4 cm and height 6cm?

```Volume of a square
= area of base * height / 3
= 42 * 6 / 3
= 16 * 6 / 3
= 32 cm3 ```
1.
2. What will be the volume of a sphere having radius 2.1cm

```Volume of a sphere
= 4 * π * radius3 / 3
= (4 / 3) * (22 / 7) * 2.13
= 38.808 cm3  ```
1.
2. What will be the surface area of a cube having side length breadth and height 8 cm?

```Surface area of a cube
= 6 * side2
= 6 * 82
= 6 * 64
= 384 cm2 ```
1.

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