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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

In the topic "mensuration" focuses on learning

 •  what is measurement standard?

 •  Absolute and Derived Standards

In this page, Finding surface area of simple figures (cube, cuboid, and cylinder) are revised without much discussion.



click on the content to continue..

Which of the following is the measure of area?

  • distance-span between two points
  • surface-span within a closed shape
  • surface-span within a closed shape
  • space-span within a closed solid

The answer is "surface-span within a closed shape"

What is a "cube"?cube surface area

  • a 3D shape with `6` square faces
  • a 3D shape with `6` square faces
  • a 3D shape with `6` rectangular faces

The answer is "a 3D shape with `6` square faces"

What is the surface area of a cube of side `a`?Surface area of cube

  • `6 xx a^2`
  • `6 xx a^2`
  • `3 xx a^2`

The answer is "`6 xx a^2`". The surface area equals the area of `6` square faces.

What is a "cuboid"?cuboid surface area

  • a 3D shape with `6` square faces
  • a 3D shape with `6` rectangular faces
  • a 3D shape with `6` rectangular faces

The answer is "a 3D shape with `6` rectangular faces"

What is the surface area of a cuboid of length `l`, breadth `b`, and height `h`?Surface area of cuboid

  • `6 xx a^2`
  • `2 xx (lb+bh+hl)`
  • `2 xx (lb+bh+hl)`

The answer is "`2 xx (lb+bh+hl)`". The surface area equals the area of `6` rectangular faces.

What is the name of the solid shape in the figure?cylinder introduction

  • cylinder
  • cylinder
  • cube

The answer is "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.oblique cylinder The right cylinder is shown in orange, and oblique cylinder is shown in blue.

What is the surface area of a cylinder of height `h` and radius `r`?cylinder surface area Note: The cylinder consists of top and bottom circular-faces and a curved surface.

  • sum of the areas of (`2` circles on top and bottom) and the area of the curved surface
  • `2 xx pi xx r^2 + 2 xx pi xx r xx h`
  • both the above
  • both the above

The answer is "both the above". The formula is explained in the next page.

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

The curved surface is visualized into a rectangle of length `2pi r` and height `h`. cylinder surface area 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 xx pi xx r^2 + 2 xx pi xx r xx h`

`=2pi r (r+h)`

Surface Area of Some Shapes: Surface Area of cube `= 6q^2` Surface Area of cuboid `= 2(lb+bh+hl)` Curved Surface Area of Cylinder `= 2pi r h` Surface Area of cylinder `=2pi r (r+h)`

Solved Exercise Problem:

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

  • `52cm^2`
  • `52cm^2`
  • `26cm^2`

The answer is "`52cm^2`"

                            
slide-show version coming soon