how to get the answer---**Question Information:**
Question 1 of 35
**Question Stem:**
A rectangular box has a volume of 50 431 cubic centimetres.
The box is 37 centimetres long and 29 centimetres wide.
What is the total surface area of the box?
**Options:**
A 1 073 square centimetres
B 2 146 square centimetres
C 4 175 square centimetres
D 8 350 square centimetres
E 10 480 square centimetres
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We have a rectangular box with a volume of 50,431 cubic centimeters. The box is 37 centimeters long and 29 centimeters wide. We need to find the total surface area of this box. First, we'll need to determine the height using the volume formula.
To find the height, we use the volume formula: V equals length times width times height. Substituting our known values: 50,431 equals 37 times 29 times h. First, we calculate 37 times 29, which equals 1,073. Then we divide 50,431 by 1,073 to get the height of 47 centimeters.
Now we use the surface area formula for a rectangular box: TSA equals 2 times the sum of lw plus lh plus wh. This accounts for all six faces of the box - there are two faces of each type. We have length equals 37 centimeters, width equals 29 centimeters, and height equals 47 centimeters. We need to calculate the area of each pair of faces.
Now we calculate the area of each type of face. Length times width equals 37 times 29, which is 1,073 square centimeters. Length times height equals 37 times 47, which is 1,739 square centimeters. Width times height equals 29 times 47, which is 1,363 square centimeters. Adding these together: 1,073 plus 1,739 plus 1,363 equals 4,175 square centimeters.
Finally, we calculate the total surface area by multiplying the sum by 2. TSA equals 2 times 4,175, which equals 8,350 square centimeters. Comparing this with the given options, our answer matches option D: 8,350 square centimeters. Therefore, the total surface area of the rectangular box is 8,350 square centimeters.