GRE Geometry | Three – Dimensional Figures

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:**

- Line
- Triangle
- Quadrilateral
- Circle

**Examples of 3-dimensional figures:**

**Cube:**

In a cube length breadth and height are all equal.length = breadth = height

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 = a

^{3}Surface area of cube = 6 * area of one face Surface area of cube = 6 * a^{2}**Cuboid:**

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 * breadth + breadth * height + breadth * height + length * height + length * height Surface area of cuboid = 2(length * breadth + breadth * height + length * height )

**Sphere:**

A sphere has radius, volume and surface area:Volume of sphere = (4 / 3) * π * radius * radius * radius Volume of sphere = (4 / 3) * π * r

^{3}Surface area of sphere = 4 * &pi * radius * radius Surface area of sphere = 4 * &pi * radius^{2}Volume of hemisphere = (2 / 3) * π * radius * radius * radius Surface area of sphere = 2 * &pi * radius * radius**Cylinder:**

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

**Cone:**

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 + π * radius * radius

**Pyramid:**

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

**Examples:**

- 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 cm

^{2} - What will be the slant height of a cone which have curved surface area 990 cm
^{2}and radius 5 cm?Curved surface area of a cone = π * radius * slant height π * radius * slant height = (22 / 7) * 5 * l l = 63cm

- 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 = 4

^{2}* 6 / 3 = 16 * 6 / 3 = 32 cm^{3} - What will be the volume of a sphere having radius 2.1cm
Volume of a sphere = 4 * π * radius

^{3}/ 3 = (4 / 3) * (22 / 7) * 2.1^{3}= 38.808 cm^{3} - What will be the surface area of a cube having side lenghth breadth and height 8 cm?
Surface area of a cube = 6 * side

^{2}= 6 * 8^{2}= 6 * 64 = 384 cm^{2}