Question

a recycling bin is in the shape of a rectangular box find the height of the box if it's length is 18 ft its width is 8 feet and its surface area is 496 ft squared.

Answer 1

we are given that

A recycling bin is in the shape of a rectangular box . Its length is 18 ft, its width is 8 feet and its surface area is 496 ft squared.

we have been asked to find the height of the box ?

As we know that the surface area of the rectangular prism is given by the formula

`A=2(wl+hl+hw)`

where l=length, w=width, h=height

Now substitute the given values we get

`496=2(8*18+h*18+h*8)`

`496=2(144+26h)`

`496=188+52h`

`496-188=52h`

`308=52h`

`h=77/13`

Hence the required height is 77/13.

Answer 2

The height of the box is:

4 ft.

Explanation:

Let "h" denotes the height of the box.

Length of box is denoted by "l"

and breadth or width of box is denoted by "b"

We are given l=18 ft

b=8 ft.

Also we are given surface area of rectangular box= 496 ft²

As we know that the surface area of box is given by:

`Surface\ Area=2(lb+bh+hl)`

i.e.

`496=2(18h+8h+144)\\\\i.e.\\\\\\496=2(26h+144)`

Divide both side by 2.

`248=144+26h\\\\i.e.\\\\26h=248-144\\\\i.e.\\\\26h=104`

on dividing both side by 26 we get:

`h=4`

Hence, the height of the box is:

4 ft.