Question

The Question says ‘ The value of the solids surface area is equal to the value of the solids volume. Find the value of x’ Please help I am really struggling on the Question!

Answer 1

The value of x is 7.5 in.

Explanation:

Consider the provided information.

Let the length of the box is x in, width 6 in and height is 5 in.

The Volume of the box is:
`length* width* height`

`Volume=x* 6* 5`

`Volume=30x`

The surface area of rectangle is:

SA = 2[(length×width)+(width×height)+(length×height)]

SA = 2[(6×x)+(6×5)+(x×5)]

SA = 2[6x+30+5x]

SA = 2[11x+30]

It is given that surface area is equal to the value of the solids volume.

30x = 2[11x+30]

15x = 11x+30

4x = 30

x = 30/4

x = 7.5

Hence, the value of x is 7.5 in.

Answer 2

1. You have that the surface area is:

`SA=2(5)(6)+2(5x)+2(6x)\\ SA=60+10x+12x\\ SA=60+22X`

2. The volume is:

`V=(6x)(5)\\ V=30x`

3. Based on the information given in the problem:

`SA=V`

4. You need to substitute values and solve for
`x` :

`22x+60=30x\\ x=7.5in`

The answer is:
`7.5in`