Question

Is it possible to change the volume of the cube without changing its height?
a. Yes.
b. No.
c. Both A and B.
d. None of the above.

Answer 1

Hint: All the sides of a cube are always equal. The volume of a cuboid having dimensions of length (l), breadth (b), height (h) is given by formula $l\times b\times h$. Considering this fact and using the formula of volume of cube get the desired result.

Complete step-by-step answer:

The volume of a cuboid having dimensions of length (l), breadth (b), height (h) is given by formula $l\times b\times h$. Now the cuboid which has all dimensions equal to ‘a’ such that ‘l = b = h = a’ is known as a cube which has a volume equal to $a\times a\times a$ .

Now we know that if any of the dimensions (length or breadth) is changed in a cuboid other than height, then volume of the cuboid will change but in the case of a cube, change in any dimension will eventually change the height also.

So, we can conclude that it is not possible to change the volume of a cube without changing the height of the cube.

In other words, we can say that it is not possible to change the volume of the cube without changing its height. So our final answer is option (b).

Note: There is a possibility of mistake when you get confused with cuboid and cube volume formula. The side dimension in case of a cube is constant while in case of cuboid it is different. The volume in case of a cube depends on only one variable but in case of cuboid it depends on three variables.