Mensuration : Length, Area, and Volume : Surface Area of Cube, Cuboid, Cylinder

maths > mensuration-basics

Surface Area of Cube, Cuboid, Cylinder

what you'll learn...

Overview

Surface Area of Some Shapes: Surface Area of cube $= 6 q^{2}$ $= 6q^2$ Surface Area of cuboid $= 2 (l b + b h + h l)$ $= 2(lb+bh+hl)$ Curved Surface Area of Cylinder $= 2 π r h$ $= 2pi r h$

Surface Area of cylinder $= 2 π r (r + h)$ $=2pi r (r+h)$

surface-area

Area is the surface-span within a closed 2D-shape. Surface-area is the area of 2D-surfaces enclosing a 3D-shape.

cube

A "cube" is "a 3D shape with $6$ $6$ square faces"

The surface area of a cube of side $a$ $a$ is " $6 \times a^{2}$ $6 xx a^2$ ". The surface area equals the area of $6$ $6$ square faces each having area $a^{2}$ $a^2$ .

cuboid

A "cuboid" is "a 3D shape with $6$ $6$ rectangular faces"

The surface area of a cuboid of length $l$ $l$ , breadth $b$ $b$ , and height $h$ $h$ is " $2 \times (l b + b h + h l)$ $2 xx (lb+bh+hl)$ ". The surface area equals the area of $6$ $6$ rectangular faces for which area is $l b + l b + b h + b h + h l + h l$ $lb + lb + bh + bh + hl + hl$

cylinder

Cylinder is a 3D shape that has circular cross-section uniformly along its axis.

When not mentioned, a cylinder is a right-cylinder with it axis at right-angle to the top and bottom faces. The other type is the oblique cylinder, in which the angle between the axis and the top (or bottom) face is not a right-angle. The right cylinder is shown in orange, and oblique cylinder is shown in blue.

The surface area of a cylinder of height $h$ $h$ and radius $r$ $r$ is sum of the areas of ( $2$ $2$ circles on top and bottom) and the area of the curved surface, which is given as $2 \times π \times r^{2} + 2 \times π \times r \times h$ $2 xx pi xx r^2 + 2 xx pi xx r xx h$

Note: The cylinder consists of top and bottom circular-faces and a curved surface.

The curved surface is visualized into a rectangle of length $2 π r$ $2pi r$ and height $h$ $h$ .

The curved surface area of the cylinder equals the area of the rectangle.

Total surface area of the cylinder

$=$ $=$ area of the circle on top and bottom $+$ $+$ area of the curved surface

$= 2 \times π \times r^{2} + 2 \times π \times r \times h$ $= 2 xx pi xx r^2 + 2 xx pi xx r xx h$

$= 2 π r (r + h)$ $=2pi r (r+h)$

example

What is the surface area of a cuboid of length $2$ $2$ cm, breadth $3$ $3$ cm, and height $4$ $4$ cm?
The answer is " $52 c m^{2}$ $52cm^2$ "

summary

Outline

The outline of material to learn "Mensuration basics : Length, Area, & Volume" is as follows.

Note: click here for detailed outline of Mensuration (Basics).

• Measuring Basics

→ Introduction to Standards

→ Measuring Length

→ Accurate & Approximate Meaures

→ Measuring Area

→ Measuring Volume

→ Conversion between Units of Measure

• 2D shapes

→ Perimeter of Polygons

→ Area of Square & rectangle

→ Area of Triangle

→ Area of Polygons

→ Perimeter and area of a Circle

→ Perimeter & Area of Quadrilaterals

• 3D shapes

→ Surface Area of Cube, Cuboid, Cylinder

→ Volume of Cube, Cuboid, Cylinder