Surface Area of Cube, Cuboid, Cylinder

Overview

**Surface Area of Some Shapes**:
Surface Area of cube $=6{q}^{2}$
Surface Area of cuboid $=2(lb+bh+hl)$
Curved Surface Area of Cylinder $=2\pi rh$

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

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 $6$ square faces"

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

cuboid

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

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

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

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

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

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

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

$=2\pi r(r+h)$

example

What is the surface area of a cuboid of length $2$ cm, breadth $3$ cm, and height $4$ cm?

The answer is "$52c{m}^{2}$"

summary

**Surface Area of Some Shapes**:
Surface Area of cube $=6{q}^{2}$
Surface Area of cuboid $=2(lb+bh+hl)$
Curved Surface Area of Cylinder $=2\pi rh$

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

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__