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

Solution:

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

Answer:

The height of the box is:

                             4 ft.

Step-by-step 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.