PLEASE ANSWER ASAP 100POINTS!!!!!
The areas of the top, the side, and the front of a
rectangular solid are x, y, and z square inches,
respectively. What is the volume of the rectangular solid, in cubic inches?

A) [tex](xyz)^{\frac{1}{3} }[/tex]
B) [tex](xyz)^{\frac{1}{2} }[/tex]
C) xyz
D) (xyz)²
E) (xyz)³

Respuesta :

Answer:

B

Step-by-step explanation:

Consider solving this a few different ways.

You can relate the surface area to the volume of the rectangular prism.

Surface area = 2*(X+Y+Z)
Volume is X*Y*Z

then algebraically you can solve for the relationship between volume and surface area.

Or you can consider units (easier way)
X, Y and Z are in inches^2

This means when X*Y*Z the units will be inches^6 for the solution (since when multiplying units the exponents get added) (in^2 * in^2 * in^2) = in^6

so knowing that you need the units to be in^3 this means that the answer must be B since (in^6)^(1/2) will equate to in^(6*(1/2)) = [tex]in^{6/2}[/tex] or in^3

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