Mensuration : Length, Area, and Volume : Revision : Cube, Cuboid, Cylinder

maths > mensuration-high

Revision : Cube, Cuboid, Cylinder

what you'll learn...

Overview

Surface Area of Some Shapes: cuboid surface area 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

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

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.

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.

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 $h$ $h$ and radius $r$ $r$ is the sum of the areas of ( $2$ $2$ circles on top and bottom) and the area of the curved surface. $= 2 \times π \times r^{2} + 2 \times π \times r \times h$ $= 2 xx pi xx r^2 + 2 xx pi xx r xx h$

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

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

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

$= 2 π r (r + h)$ $=2pi r (r+h)$

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

Surface Area of Some Shapes: cuboid surface area 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 $= 2 π r (r + h)$ $=2pi r (r+h)$

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