The area of one face of a cube is x square meters, which of the following gives an expression for the volume?

Question

of this cube, in cubic meters?

i'm cluless. the book says sq.root x times x

Answer 1

effectively if the area of one face is x square meters one side has a length of x^1/2 (= square root) the volume is the side at power 3 so (x^1/2)^3 = x^1.5 and x^1.5 = x*x^0.5

Answer 2

The volume of the cube is the length of any edge to the third power. Therefore, the square root of x (x being the area) would give you the length of one edge. That number to the third power, or cubed, would give you the volume, in cubic meters.

expression: (square root of x) to the 3rd power
(I can't write the signs...)

Answer 3

The area of one face of the cube is x square meters. The formula for area of a square is:

A = s^2

So, if this is equal to x, we have that

x = s^2
==> square root both sides
√x = s

So, each side is equal to √x, so we can use the volume formula where length, width, and height are all equal to √x and find the volume

V = length*width*height
==> substitute √x for all dimensions
V = (√x)(√x)(√x)
==> combine two square roots of x to just equal x
V = √(x)*x ... ANSWER

Answer 4

If the area of a cube is x square meters, then a side is
(x)^(0.5).

The formula for a volume is side to the third power.

In this case it is (x^(0.5))^3

Answer 5

the thing to realize is that they told you the area of one face is x sq meters.

NOT the length of one side is x meters.

the formula for the area of a square is s^2 where s is the length of the side
the formula for the volume of a cube is s^3 where s is the length of the side

so if the area is x, x=s^2, which means the length of the side is sqrt(x) : take the sqrt of both sides of the = sign.

If the side is sqrt(x) then the volume is (sqrt(x))^3
(x^a)(x^b)=x^(a+b)
(sqrt(x))^3=(sqrt(x))^2(sqrt(x))^1
(sqrt(x))^2=x and (sqrt(x))^1=sqrt(x) so
(sqrt(x))^3=x(sqrt(x))

Answer 6

The volume of a rectangular object is V=L*W*H.
Since the object here is a cube, L=W=H=sqrt(x).
This is because the area of one face, A=L*W=x, and L=W.
Therefore, L=W=sqrt(x).
Then V=sqrt(x)*sqrt(x)*sqrt(x)= x*sqrt(x) = x^(3/2)

Answer 7

yes the book is correct.
Square root of X multiplied by X, cant be simplified any further