Solid Mensuration
* Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
As the volume of a cube is the third power of its sides , third powers are called cubes, by analogy with squares and second powers.
A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).
* Parts:
Side/ lateral Face Height (s) Bases
* formulae:
Surface Area= 6s2
Volume: s3
Face Diagonal:
Space Diagonal:
Radius of Circumscribed Sphere:
Radius of sphere tangent to edges
Radius of inscribed sphere
Angles between faces (in radians)
Questions:
1. What is the volume of a cube with sides of length of 6 cm?
2. How many dices with sides of 1.8 cm in length will fit in a cube box with side of 30 cm in length?
* Cuboid/ Rectangular prism
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While some mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.
In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism.
* Parts: Rectangular cuboid
length width
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
As the volume of a cube is the third power of its sides , third powers are called cubes, by analogy with squares and second powers.
A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).
* Parts:
Side/ lateral Face Height (s) Bases
* formulae:
Surface Area= 6s2
Volume: s3
Face Diagonal:
Space Diagonal:
Radius of Circumscribed Sphere:
Radius of sphere tangent to edges
Radius of inscribed sphere
Angles between faces (in radians)
Questions:
1. What is the volume of a cube with sides of length of 6 cm?
2. How many dices with sides of 1.8 cm in length will fit in a cube box with side of 30 cm in length?
* Cuboid/ Rectangular prism
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While some mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.
In a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism.
* Parts: Rectangular cuboid
length width