__maths__>__Mensuration : Length, Area, and Volume__>__Mensuration: Three Dimensional Shapes__### 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.

*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"?

- 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`"

*slide-show version coming soon*