Question - Calculating Surface Area of an Open Rectangular Box
Solution:
To solve this problem, you need to find the surface area of the given 3D shape, which resembles an open rectangular box without the top.The surface area of this open box will be the sum of the areas of its five sides: the bottom, two longer sides (front and back), and two shorter sides (left and right).Here are the calculations for each part:- Bottom: $$10 \text{ in} \times 8 \text{ in} = 80 \text{ in}^2$$- Front side: $$10 \text{ in} \times 4 \text{ in} = 40 \text{ in}^2$$- Back side: $$10 \text{ in} \times 4 \text{ in} = 40 \text{ in}^2$$ (same as the front side)- Left side: $$8 \text{ in} \times 4 \text{ in} = 32 \text{ in}^2$$ (this is given as the 6-inch side, but based on the diagram it seems this is inconsistent with the 3D perspective drawing which shows it as the same as the right side which is 4 inches. We'll assume side lengths consistent with a rectangular box.)- Right side: $$8 \text{ in} \times 4 \text{ in} = 32 \text{ in}^2$$Now add them up to get the total surface area:$$80 \text{ in}^2 + 40 \text{ in}^2 + 40 \text{ in}^2 + 32 \text{ in}^2 + 32 \text{ in}^2 = 224 \text{ in}^2$$It looks like the answer we calculated, $$224 \text{ in}^2$$, is not in the provided options. It's possible there may be a mistake in the diagram or the question options provided. However, if we follow the measurements given regardless of the potential inconsistency with the diagram's perspective, the calculation would be different for the left and right sides:- Left side: $$8 \text{ in} \times 3.5 \text{ in} = 28 \text{ in}^2$$- Right side: $$8 \text{ in} \times 3.5 \text{ in} = 28 \text{ in}^2$$Then the total surface area would be:$$80 \text{ in}^2 + 40 \text{ in}^2 + 40 \text{ in}^2 + 28 \text{ in}^2 + 28 \text{ in}^2 = 216 \text{ in}^2$$It seems there is still no match among the options. There might be a misprint or error in the options or the diagram provided. If this is an exercise from a book or other resource, it may be useful to double-check any errata that might clarify the situation.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com