Question

Is it possible to find a value of $x$x​ so that the value of the surface area (in square inches) is equal to the value of the volume (in cubic inches)? A rectangular prism with length labeled x inches, width labeled 6 inches, and height labeled 3 inches.

Answer 1

Answer:

No, it’s not possible according to calculations

Step-by-step explanation:

Mathematically, the area of a rectangular prism is;

2(wl + wh + lh)

Where w is the width, l is the length and h is the height;

Making the substitutions with values in the question

Surface area = 2(6x + 3x + 3(6))

Surface Area = 2(9x + 18) = 18x + 36 square inches

Volume of rectangular prism = l * w * h

Making substitutions;

V = x * 6 * 3 = 18x cubic inches

So therefore to get the value of x, we equate the surface area to the volume;

18x = 18x + 36

We can see that 18x will cancel out and will render our equation invalid