Volume of Regularly-shaped Solids is a volume with a definite mathematical expression to calculate. according to oxford dictionary, solid means hard or firm. A regularly shaped solid is an object with a definite shape that can always be described. Each regularly shaped solid have a known geometrical shape and hence can be identified by name.
Some of the common known regular solids includes:
Volume of Regularly-shaped Solids: Cube
A cube is a six sided object with all its edges equal in length. A cube has a solid shape with six square faces all equal in area and lengths.
The volume of a cube (Vcube) is given by:
where l is the length of the edge of the cube.
Volume of Regularly-shaped Solids: cuboid
A cuboid is an object with six faces. Each pair of opposite faces is equal in shape and size. Cuboid means “like a cube” because it has the same shape as a cube. Still, not all its sides are equal.
The figure below shows a cuboid. One edge is named length. Another edge is named width. The other edge is named height.
Volume of a cuboid (Vcuboid) will be given by Vcuboid = Length x Width x Height
Volume of Regularly-shaped Solids: Cylinder
A cylinder is a three dimensional object consisting of two parallel circular surfaces that are connected by a curved surface. The distance between the two circular faces is fixed. It is usually referred to as the height of the cylinder. There is an imaginary line that passes through the center of the circles. This line is perpendicular to the circles and is known as the axis.
Volume of a cylinder (Vcylinder) is given by Vcylinder = BaseArea(BA) x height(h) where BaseArea is the area of one of the circular face given by Area (A) = πr2 hence Vcylinder = πr2 h
Volume of Regularly-shaped Solids: Sphere
A sphere is a geometrical object that is round in shape. It is defined in a three-dimensional space without any face.
Volume of a sphere (Vsphere) will be given by ;
Vsphere = (4/3)πr3
where r the radius and π a mathematical constant.
Volume of Regularly-shaped Solids: Cone
A cone is a three-dimensional shape. It has a flat circular base and a curved surface that forms a sharp point at the top. The sharp point is called the vertex.
The three parts that makes a cone are its radius, height, and slanting height. Radius r is the distance from the center of the circular base. It extends to any point on the circumference of the base.
The slant-height l is the distance from the vertex of the cone to any point on the circumference of the circular base.
The height h of a cone is the distance between the vertex and the center of the circular base.
Figure below illustrates a cone
Volume of a cone (Vcone) will be given by Vcone = (1/3) πr2h.
but πr2h = volume of a cylinder.
hence Vcone = (1/) x Volume of a cylinder
Volume of Regularly-shaped Solids: Prisms
A prism is a three-dimensional object. It has two similar surfaces facing each other. These surfaces are usually referred to as the bases of a prism. The base of the prism is usually called the cross-sectional area.
Length of the prism is distance between the two similar surfaces.
The base of the prism can assume varied shapes hence we have different types of prisms like:
- square prism
- triangular prism
- rectangular prism
- pentagonal prism
- hexagonal prism
- octagonal prism
- nonagonal prism
- decagonal prism
- hendecagonal prism
- Dodecagonal prism
- tridecagonal/triskaidecagonal prism
- tetradecagonal prism
- pentadecagonal prism
- e.t.c.
To get the volume of the prism, you first find the area of the base. Then, you multiply it by the length of the prism. hence
volume a prism = cross-section Area(A) x length (l).
Volume of a Hexagonal prism
The hexagonal prism is a prism with hexagonal base. The word hexagonal comes from the word hexagon. In geometry, a hexagon is a six-sided polygon.
To find the volume of a Hexagonal prism, calculate the area of the hexagonal base first. Then multiply this area by the length between the two hexagonal ends.
A regular hexagon has six sides each with the same length. By drawing lines from the vertices to the center of the hexagon, you can create six isosceles triangles. The area of the hexagon is equal to area of one triangle multiplied by number of triangles.
Related posts
- Volume of Regular Objects
- Introduction to volumes
- Physical Quantities
- Reading a meter rule
- Measuring with a meter rule
- Area
- Area of irregularly shaped surfaces
- Volume
- Volume of regularly shaped objects
- Measuring volume of liquids
- Volume of irregular solids
- Measuring Mass
- Density
- Densities of some substances
- Questions on Measurements
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- Measuring Volume
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