Revision : 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

The area of a shape is the "surface-span within the closed plane figure".

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.

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.

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 surfaces in the cylinder consists of top and bottom circular-faces and a curved surface. The surface area of a cylinder of height $h$ and radius $r$ is the sum of the areas of ($2$ circles on top and bottom) and the area of the curved surface. $=2\times \pi \times {r}^{2}+2\times \pi \times r\times h$

Cylinder of height $h$ and radius $r$ is shown in the figure.

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

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

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

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 : Length, Area, and Volume* is as follows.

Note 1: * click here for the detailed overview of Mensuration High *

Note 2: * click here for basics of mensuration, which is essential to understand this. *

• ** Basics of measurement**

→ __Summary of Measurement Basics__

→ __Measurement by superimposition__

→ __Measurement by calculation__

→ __Measurement by equivalence__

→ __Measurement by infinitesimal pieces__

→ __Cavalieri's Principle (2D)__

→ __Cavalieri's Principle (3D)__

• **Perimeter & Area of 2D shapes**

→ __Circumference of Circles__

→ __Area of Circles__

• **Surface area & Volume of 3D shapes**

→ __Prisms : Surface Area & Volume__

→ __Pyramids : Surface Area & Volume__

→ __Cone : Surface Area & Volume__

→ __Sphere : Surface Area & Volume__

• **Part Shapes **

→ __Understanding part Shapes__

→ __Circle : Sector and Segment__

→ __Frustum of a Cone__