Surface Area of Cube, Cuboid, Cylinder
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.
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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"?
- 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`?
- `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"?
- 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`?
- `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
- 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. 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`? 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`. 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`"