Question

Two cubes of side 8 cm are joined end to end. Find the volume of the resulting cuboid.

Answer 1

Hint:
Here we will first find the new length of the cuboid formed by adding the side of the cube. Then we will find the breadth and height of the cuboid formed which is equal to the side of the cube. Then we will use the formula of the volume of a cuboid and substitute all the values of the dimensions in the formula. We will solve it further to get the volume of the resulting cuboid.

Formula used:
We will use the formula of Volume of a cuboid \[ = {\rm{length}} \times {\rm{Breadth}} \times {\rm{Height}}\]

Complete Step by step Solution:
The side of the cubes is 8 cm.
It is given that these cubes are joined end to end to form a cuboid.
Firstly we will find the new length of the cuboid formed and new breadth and new height of the cuboid formed. Therefore, we get
New length of the cuboid formed \[ = 2 \times {\rm{side}}\]
\[ \Rightarrow \] New length of the cuboid formed \[ = 2 \times 8 = 16cm\]
We know that the breadth and height of the cuboid will remain the same. Therefore, we get
New breadth of the cuboid formed \[ = {\rm{side}} = 8cm\]
New height of the cuboid formed \[ = {\rm{side}} = 8cm\]
Now we will use the basic formula of the volume to find the volume of the cuboid. Therefore, we get
Volume of the cuboid \[ = {\rm{length}} \times {\rm{Breadth}} \times {\rm{Height}}\]
Now we will put the values in the equation, we get
\[ \Rightarrow \] Volume of the cuboid \[ = 16 \times 8 \times 8\]
Multiplying the terms, we get
\[ \Rightarrow \] Volume of the cuboid \[ = 1024c{m^3}\]

Hence the volume of the resulting cuboid is equal to \[1024c{m^3}\]

Note:
We need to keep in mind that when one or more cubes are joined then it takes the shape of a cuboid. A Cube is a shape with six flat surfaces, eight vertices or corners, and twelve edges. The length of all these edges is equal to each other. Angles made by the two consecutive sides and the edges or sides are \[{\rm{90}}^\circ \]. The Cube is the most symmetric in all hexahedron shape objects.
As the shape becomes cuboid, we will use the formula of volume of a cuboid. Volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic units.