We all know that geometry is the subject that studies about shapes and figures. There are two types of shapes around us - geometrical shapes and non geometrical shapes. Geometrical shapes are the shapes that have predefined properties explained for that particular type of shape. While, a non geometrical shape is not predefined and does not have common properties. The classification of geometrical figures on the basis of dimensions is as follows -
(1) Zero dimensional shape - A point.
(2) One dimensional shape - A line having a length as its dimension.
(3) Two dimensional shapes - Having length and breadth as two dimensions. For example - square, triangle, rectangle, parallelogram, trapezoid, rhombus, quadrilateral, polygon, circle etc.
(4) Three dimensional shapes - With length, breadth and width (height) as three dimensions. For example - cube, cuboid, cone, cylinder, sphere, pyramid, prism etc.
(5) Higher dimensional shapes - There are few shapes in expressed in dimensions higher than 3, but we usually do not study them in middle-level mathematics.
Solid is one of the major states of matter. It is characterized by structural rigidity and resistance to change of shape or volume. In geometry, the structure that is in three (even higher) dimension, are known as solids or geometric solids. The study of the properties, volume and surface area of solid objects is called as solid geometry. Let us go ahead and focus more on study of geometrical solids.
Geometric Solids Names | Solid Figures |
Description |
Cube | Solid whose faces are square. It has 8 vertices and 12 edges. | |
Cuboid | Solid whose faces are rectangular. It has 8 vertices and 12 edges. | |
Sphere | It is a circular object. | |
Cylinder | Cylinder has two flat surfaces and one curved surface. | |
Cone | Cone formed by the locus of all straight line segments that join the apex to the base. It has one curved surface and one flat surface. |
There are different types of solids that are classified based on their shapes. The different types of solids are as follows:
Cube:
Volume of a cube = a^{3} cubic units
Surface area of a cube = 6a^{2} square units
Cylinder:
Volume of a cylinder = $\pi r^2 h$ cubic units
Surface area of a cylinder = $2 \pi r(r + h)$ square units
Cone:
Volume of a cone = $\frac{1}{3}$$ \pi r^2 h$ cubic units
Surface area of a cone = $\pi r (r + l)$ square units
Sphere:
Volume of a sphere = $\frac{4}{3}$$\pi r^3$ cubic units
Surface area of a sphere = $4 \pi r^2$ square units
Given below are some pictures of 3D solids.Given below are some of the examples on solids.
Find the volume and surface area of a solid object whose each side length is equal to 5.3 centimeter.
The given solid object is a cube.
The volume of cube = a^{3} cubic units
= 5.3 * 5.3 * 5.3
= 148.877
The surface area of cube = 6 a^{2} square units
= 6 * 5.3 * 5.3
= 168.54
So, the volume and surface area of the given solid object are 148.877 cubic centimeter and 168.54 square centimeter respectively.
Find the volume and surface area of a cylinder with radius, 3.6 centimeter and height, 5.6 centimeter.
The volume of cylinder = $\pi r^2 h$
= 3.14 * 3.6 * 3.6 * 5.6
= 227.89
Volume of cylinder = 227.89 cubic centimeter
The surface area of cylinder = $2 \pi r(r + h)$
= 2 * 3.14 * 3.6(3.6 + 5.6)
= 2 * 3.14 * 3.6 * 9.2
= 207.99
Surface area = 207.99 square centimeter
So, the volume and surface area of the given cylinder are 227.89 cubic centimeter and 207.99 square centimeter.
Find the volume of a cone, with radius 3 cm and height 9 cm.
The volume of cone = $\frac{1}{3}$$\pi r^2 h$ cubic units
= $\frac{1}{3}$ * 3.14 * 3 * 3 * 9
= 84.78
Thus, the volume of a cone is 84.78 cubic cm.
More topics in Solids | |
Volume Formula | Lateral Area |
Cross Section | Cube |
Hemisphere | Cone |
Cuboid | Cylinder |
Sphere | Prism |
Pyramid | Similar Solids |
Polyhedron | Surface Area and Volume of Combination of Solids |
Related Topics | |
Math Help Online | Online Math Tutor |