A shipping box has a surface area of 369.5 in2, a height of 9.5 inches, and a width of 3 inches. What is the length of the box? Round the answer to the nearest hundredth.
First, we need to set up the formula for surface area of a rectangular prism:
SA = 2lw + 2lh + 2wh
We know SA = 369.5 in², h = 9.5 in, and w = 3 in. We can plug in these values and solve for l:
369.5 = 2(l)(3) + 2(l)(9.5) + 2(3)(9.5)
369.5 = 6l + 19l + 57
369.5 = 25l + 57
312.5 = 25l
l = 12.50
Therefore, the length of the box is approximately 12.50 inches.
To find the length of the box, we need to use the formula for the surface area of a rectangular prism. The formula is:
Surface Area = 2(length × width) + 2(length × height) + 2(width × height)
We are given that the surface area is 369.5 in2, the height is 9.5 inches, and the width is 3 inches. Let's substitute these values into the formula:
2(length × 3) + 2(length × 9.5) + 2(3 × 9.5) = 369.5
Simplifying the equation, we have:
6(length) + 19(length) + 57 = 369.5
Combining like terms, we get:
25(length) + 57 = 369.5
Subtracting 57 from both sides, we have:
25(length) = 312.5
To isolate the length, we divide both sides by 25:
length = 312.5 / 25
length = 12.5
Therefore, the length of the box is 12.5 inches.
To find the length of the box, we need to rearrange the formula for calculating the surface area of a rectangular box. The formula is:
Surface Area = 2lw + 2lh + 2wh
Given that the surface area is 369.5 in², the height (h) is 9.5 inches, and the width (w) is 3 inches, we can substitute these values into the equation and rearrange it to solve for the length (l):
369.5 = 2lw + 2(9.5)w + 2(3)h
Since we're looking for the length, we need to isolate it on one side of the equation.
First, let's simplify the equation:
369.5 = 2lw + 19w + 6h
Next, we'll substitute the known values:
369.5 = 2l(3) + 19(3) + 6(9.5)
Now, we can simplify further:
369.5 = 6l + 57 + 57
369.5 = 6l + 114
Now, let's isolate "l" by subtracting 114 from both sides:
369.5 - 114 = 6l
255.5 = 6l
Finally, divide both sides by 6 to solve for l:
255.5/6 = l
l ≈ 42.58
Therefore, the length of the box is approximately 42.58 inches when rounded to the nearest hundredth.