# If the edge of the cube is doubled, then its volume:

(a) Is doubled

(b) Becomes 4 times

(c) Becomes 6 times

(d) Become 8 times

Answer

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Hint: To solve the question, we have to apply the formula of the volume of a cube for the given edge length and then compare the obtained values to reach the answer.

Complete step-by-step answer:

Let x be the edge of the cube.

The edge of the cube when it is doubled = 2$x$

We know that the volume of a cube with the length of the edge as x, is given by the formula \[{{x}^{3}}\] cubic units.

Thus, the volume of a cube with length of edge as 2$x$ \[={{\left( 2x \right)}^{3}}\]

\[={{2}^{3}}\times {{x}^{3}}\]

\[=8{{x}^{3}}\] cubic units.

The above value is 8 times \[{{x}^{3}}\], which is equal to the volume of the cube with edge x.

Thus, the obtained volume with the edge being doubled is equal to 8 times the volume of a cube with edge $x$.

Hence, the option (d) is the right choice.

Note: The possible mistake can be analysing that the volume will be doubled too since the edge of the cube is doubled, but the side of the cube should be cubed to obtain the volume of the edge which is doubled. The alternative quick method of solving is assuming a certain value for x, which will ease the procedure of solving. The alternative method of solving the question is option elimination, we know that volume of a cube is cube of edge length which implies the changed volume will also be in the form of cube, in the given option only 8 is a cube. Thus, other options can be eliminated.

Complete step-by-step answer:

Let x be the edge of the cube.

The edge of the cube when it is doubled = 2$x$

We know that the volume of a cube with the length of the edge as x, is given by the formula \[{{x}^{3}}\] cubic units.

Thus, the volume of a cube with length of edge as 2$x$ \[={{\left( 2x \right)}^{3}}\]

\[={{2}^{3}}\times {{x}^{3}}\]

\[=8{{x}^{3}}\] cubic units.

The above value is 8 times \[{{x}^{3}}\], which is equal to the volume of the cube with edge x.

Thus, the obtained volume with the edge being doubled is equal to 8 times the volume of a cube with edge $x$.

Hence, the option (d) is the right choice.

Note: The possible mistake can be analysing that the volume will be doubled too since the edge of the cube is doubled, but the side of the cube should be cubed to obtain the volume of the edge which is doubled. The alternative quick method of solving is assuming a certain value for x, which will ease the procedure of solving. The alternative method of solving the question is option elimination, we know that volume of a cube is cube of edge length which implies the changed volume will also be in the form of cube, in the given option only 8 is a cube. Thus, other options can be eliminated.

Last updated date: 25th Sep 2023

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