I really need help with this Question. The question says ‘ The value of the solid’s surface are is equal to the value of the solid’s volume. Find the value of x.’

Units of square inches are never equal to units of cubic inches, so we presume the statement of the problem applies to the numerical values in in² and in³.

The volume of a cuboid of length L, width W, and height H is

... V = LWH

The area is

... A = 2(LW + H(L+W))

You want these to be equal for L=9, W=4, and H=x.

Equating the expressions, we have

... 9·4·x = 2(9·4 +x(9+4))

... 36x = 2(36 +13x) . . . . . simplify a bit

... 36x = 72 + 26x . . . . . . simplify more

... 10x = 72 . . . . . . . . . . . . subtract 26x

... x = 7.2

The dimension represented by x is 7.2 inches.

jdoe0001 jdoe0001 · Answer 2 · 2018-09-16T21:31:14+02:00

the gift-box above, is pretty much just a rectangular prism, like the one in the picture below, check the picture below.

so as you can see, is really just 6 rectangles stacked up to each other at the edges.

to get the area of the gift-box, we simply get the area of all rectangles.

left and right, is just 2 rectangles of 4*x, or 2(4*x) = 8x.

front and back, is 2 rectangles of 9*x, or 2(9*x) = 18x.

top and bottom, is 2 rectangles of 9*4, or 2(9*4) = 72.

if we sum those up, that's the surface area, SA, of the gift-box, 8x + 18x + 72.

now its volume is simply the product of the height, length and width, namely 9*4*x, or 36x.

[tex]\bf SA=V\implies \stackrel{SA}{8x+18x+72}~~=~~\stackrel{V}{36x}\implies 26x+72=36x \\\\\\ 72=36x-26x\implies 72=10x\implies \cfrac{72}{10}=x\implies \cfrac{36}{5}=x\implies \boxed{7.2=x}[/tex]