Find the volume of 64 cubes whose one side is 4cm

Mensuration is a subject under geometry. Mensuration deals with the size, region, and density of different forms in both 2D and 3D. 3D shapes are structures surrounded by a variety of surfaces or planes. Unlike 2D shapes, these shapes have height or depth; they have three-dimensional length, breadth, and height/depth and are thus called 3D shapes. 3D shapes are made up of a number of 2D shapes, Often known as strong forms, volume, curved surface area, lateral surface area, and complete surface area are measured for 3D shapes.

Volume

Volume is the quantity present in a three-dimensional space enclosed by a surface. For instance, the space/amount that a substance or a 3D shape occupies or contains. Volume is usually quantified numerically using the SI-derived unit, the cubic meter. The volume of the liquid is usually measured in liters.

The volume of a cube is the total amount of three-dimensional space occupied by a cube. A cube is a 3-D structure with six square faces, having all its sides of the same length. The cube is also called a regular hexahedron. The unit of volume of the cube is given as cubic units. The SI unit of volume is called the cubic meter (m³), which is the volume occupied by a cube with each side of length equal to 1m. 

Find the volume of 64 cubes whose one side is 4cm

The objective here is to find the Volume of 64 cubes with one side of length 4cm. It can be calculated using the side length or by using the measure of the cube’s diagonal.

Method 1 Using Side length

The volume of a cube can be found by multiplying the side length three times. In the above-mentioned cube, the side length is 4cm. Therefore the volume is 4 × 4 × 4 = 64 cm³. Now there are 64 cubes, each of which occupies the same volume as the other. This means 64 cm³ is added 64 times to obtain the volume of 64 cubes that is 64 × 64 = 4,096 cm³.

Method 2 Using Diagonal

The volume of the cube can also be found by another formula if the diagonal is known. The diagonal of the cube is root3*a where a is the side length of the cube. The Volume of the cube has the formula root3 d^3/9 where d is the diagonal length

In this case, the volume of one cube is 64 cm³ (because diagonal = √(3 × 4) cm) 

Therefore, the volume of 64 cubes is 4,096 cm³

Similar Problems

Question 1: What is the volume of a cube of side 3 cm?

Solution:

Side of the cube a = 3 cm

Volume of a Cube formula is V = a³

V= 3³ cm3

∴ V = 27 cm³

Question 2: What is the volume of a cube of side 6 cm?

Solution:

Side of the cube a = 6 cm

Volume of a cube is V = a³

V = 6³ cm³

V = 216 cm³

Question 3: What is the volume of a cube of side 2 cm?

Solution:

Side of the cube a = 2 cm

Volume of a cube = a³ cm³

V = 2³ cm³

V = 8 cm³