Use the five steps for problem solving to answer the following question. Please show all of your work.
The volume of a rectangular box is limited to 1100 cu. in. If the height is 8 inches and the width is 10 inches how long can the box be?
V=Volume
L=Lenght
H=Hight
W=L*W*H
1100=L*10*8
1100=80*L Divide booth sides with 80
L=1100/80=13.75 in
Sure! To answer this question using the five steps for problem solving, let's go through each step:
Step 1: Understand the Problem
The problem states that the volume of a rectangular box is limited to 1100 cubic inches. We are given the height of 8 inches and the width of 10 inches. We need to find the length of the box.
Step 2: Devise a Plan
To find the length of the box, we can use the formula for the volume of a rectangular box:
Volume = Length * Width * Height
Since we know the volume, height, and width, we can rearrange the formula to solve for the length:
Length = Volume / (Width * Height)
Step 3: Carry Out the Plan
Plugging in the given values:
Length = 1100 cu. in. / (10 in. * 8 in.)
Length = 1100 cu. in. / 80 sq. in.
Length = 13.75 inches
Step 4: Evaluate the Result
After evaluating the calculation, we find that the length of the box can be 13.75 inches.
Step 5: Check the Answer
To check the answer, we can substitute the calculated length back into the volume formula and see if it equals 1100 cubic inches:
Volume = Length * Width * Height
Volume = 13.75 in. * 10 in. * 8 in.
Volume = 1100 cu. in.
Since we obtain the original volume of 1100 cubic inches, we can conclude that our answer is correct.
Therefore, the box can be 13.75 inches long.