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# Cubes

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 Sub Topics Cubes in maths is a Solid geometrical shape, whose all sides are of equal length means length, width and height of cubes are of equal length. All sided (length, height and width) of cubes are defined in 3d (3 dimension), that’s why we call this solid Geometry as a cubes in 3d. Now we discuss geometry of cube. Each cube made by 6 squares which meet at right angles means if we connect 6 squares at right angles, then produced geometry is known as cube geometry and each cube has 8 vertices and 12 edges. So, cube is a 3d geometry. Now we discuss formulas for calculating volume and surface area of cubes: Volume of cubes = a * a * a, Here ‘a’ is length of cube, ‘a’ is height of cube and a is width of cube, Surface area of cubes = 6 * a2, Here ‘a’ is length of cube, ‘a’ is height of cube and ‘a’ is width of cube, Suppose, we have a cube, whose length, height and width is equal to 5 inch, then– Volume of cube = a * a * a, = 5 * 5 * 5, = 125 inch3. Surface area of cube = 6 * a2, = 6 * (5)2, = 6 * 25, = 150 inch2. So, volume of cube is 125 inch3 and Surface Area of Cube is 150 inch2, where length, height and width are equals to 5 inch. All three sides length, width and height of cubes are define in 3 d geometry like here in above example length, width and height of cubes are 5 inch are define in 3 dimension and volume of given cube is 125 inch3 and surface area of this 3d solid geometry, which is called as a cube is 150 inch2. This is all about 3d cube geometry.

## Surface Area of Cube

Cube can be defined as a 3 dimensional object, which consists of 6 faces and each face has equal dimensions or we can also say that Cube consists of 6 squares of equal dimensions or sides.

Let us now see what is Surface Area Of Cube, it can be as combined area of all the faces of the cube or combined area of all 6 Square faces.

Area of one face of a cube is given by a2, where ‘a’ is the length of the face of cube, therefore The Surface Area Of A Cube can be calculated by adding area of all 6 faces of cube.

Area of one face is a2 as we calculated earlier, so surface area of cube is given by:
Surface area of cube = (a2 +a2 + a2 + a2 + a2 + a2) = 6a2.
Therefore surface area of a cube equals to six multiplied by square of its side or 6 a2.

Suppose we have to calculate the surface area of a cube whose side length is equals to 18 inch.
First we will square the side we get,
a2 = a * a = 18 * 18 = 324.
We know that Surface Area Cube is equals to 6a2, therefore we get,
Surface area of cube = 6a2 = 6 * 182 = 6 * 324 = 1944 inch2.
Therefore surface area of cube is equals to 1944 inch2.

Now calculate the surface area of a cube whose side length is equals to 2 inch.
First Square the side = a2 = 2 * 2 = 4,
Now multiply a2 by 6a2, we get
6a2 = 6 * 2 * 2 = 24 inch2,
Therefore surface area of this cube is equals to 24 inch2.
This is how we calculate the surface area of cube.