Question

Devon made a box with length x+1, width x+3, and height x-3. What is the volume of Devon's box as a function of x?

what is x if volume of box is equal to 1001 cubic inches?
what is x if volume of the box is equal to 14 5/8 cubic inches?

Answer 1

(a)

`V=x^3+x^2-9x-9`

(b)

`x=10`

(c)

`x=(7)/(2)`

Explanation:

we are given

length is x+1

`L=x+1`

width is x+3

`W=x+3`

height is x-3

`H=x-3`

(a)

we can use volume formula

`V=L* W* H`

now, we can plug it

`V=(x+1)* (x+3)* (x-3)`

now, we can simplify it

`V=x^3+x^2-9x-9`

(b)

we are given volume =1001

so, we can set V=1001

and then we can solve for x

`V=x^3+x^2-9x-9=1001`

now, we can factor it

`\left(x-10\right)\left(x^2+11x+101\right)=0`

`x-10=0`

`x=10`

(b)

we are given volume

so, we can set

`V=14(5)/(8)=(14* 8+5)/(8)`

`V=(117)/(8)`

and then we can solve for x

`V=x^3+x^2-9x-9=(117)/(8)`

now, we can factor it

`8x^3+8x^2-72x-189=0`

`\left(2x-7\right)\left(4x^2+18x+27\right)=0`

`2x-7=0`

`x=(7)/(2)`