Question

the volume of a 15oz cereal box is 180.4in cube. the length of the box is 3.2 in. less than the height and the width is 2.3 in. find the height and length of the box to the nearest tenth.

Answer 1

The height and length of the box to the nearest tenth will be 10.6 inch and 7.4 inch respectively.

Step-by-step explanation

Suppose, the height of the box is
`h` inch

As the length of the box is 3.2 in. less than the height, so the length will be:
`(h-3.2) inch`

Given that, the width of the box is 2.3 inch. and the volume is 180.4 inch³

Formula for Volume of a box:
`V= length*width*height`

So, the equation will be....

`(h-3.2)*2.3*h = 180.4\\ \\ 2.3h^2 -7.36h=180.4\\ \\ 2.3h^2-7.36h-180.4=0`

Now using quadratic formula......

`h=(-b+/-√(b^2-4ac))/(2a)\\ \\ h= (-(-7.36)+/-√((-7.36)^2-4(2.3)(-180.4)))/(2(2.3))\\ \\ h= (7.36+/-√(1713.8496))/(4.6) \\ \\ h=(7.36+/-41.398...)/(4.6) \\ \\ h= 10.599... or -7.399...`

(Negative value of
`h` is ignored as the height can't be negative)

So, the height to the nearest tenth will be 10.6 inch and the length will be:
`(10.6-3.2)inch= 7.4 inch`