Questions: A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 6 ft, and its surface area is 456 ft². (In the figure, h=height, l=length, w=width of the box.)

A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 6 ft, and its surface area is 456 ft². (In the figure, h=height, l=length, w=width of the box.)

Transcript text: A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 6 ft, and its surface area is 456 ft². (In the figure, h=height, l=length, w=width of the box.)

Solution

Solution Steps

Step 1: Write the formula for the surface area of a rectangular box

The surface area (SA) of a rectangular box is given by the formula: SA = 2(lw + lh + wh), where l is the length, w is the width, and h is the height.

Step 2: Substitute the given values into the formula

We are given that the length l = 18 ft, the width w = 5 ft, and the surface area SA = 456 ft². Substituting these values into the formula, we get:

456 = 2(18 * 5 + 18 * h + 5 * h)

Step 3: Simplify and solve for h

456 = 2(90 + 18h + 5h) 456 = 2(90 + 23h) 456 = 180 + 46h 276 = 46h h = 276 / 46 h = 6

Final Answer:

The height of the box is 6 ft.

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