
The length of diagonal of a cube is 17.32 cm, find the volume of the cube.
Answer
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Hint: First, we need to find the length of the diagonal of a cube in terms of its side. Next, find the side of the cube and hence find the volume of the cube.
Complete step by step answer:
The formula of the length of the diagonal of the cube is shown below.
Here, is the length of the side of the cube.
Since, the diagonal of the cube is 17.32 cm, substitute 17.32 for in equation (1) to obtain the length of the side of the cube.
The formula for the volume of the cube having side length is shown below.
Substitute, 10 for in equation (2) to obtain the volume of the cube as follows:
Thus, the volume of the cube is .
Note: We can use Pythagoras theorem to obtain the length of the diagonal of the cube. In the cube all the diagonals are of equal length. There are six face diagonals of the cube having length 1.414 times its side length.
Complete step by step answer:
The formula of the length

Here,
Since, the diagonal of the cube is 17.32 cm, substitute 17.32 for
The formula for the volume
Substitute, 10 for
Thus, the volume of the cube is
Note: We can use Pythagoras theorem to obtain the length of the diagonal of the cube. In the cube all the diagonals are of equal length. There are six face diagonals of the cube having length 1.414 times its side length.
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