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Formula for Cuboid Surface Area Used to Determine Cost of Making Closet

Formula for Cuboid Surface Area Used to Determine Cost of Making Closet
The teacher helps the small groups of students as they calculate the area of the net of a cuboid using an old packaging box.

TANGERANG, BANTEN – Akidin MPd, a math teacher at MTsN Tigaraksa Banten, invited his Grade 8 students to find the formula to calculate the surface area of a cuboid so that they could apply it to solving problems in everyday life.

The teacher began the lesson by showing the students a picture and asking them what it showed. " Medicine boxes," said one student. "What are their shape?" Asked Akidin. "There is a cube and there is a cuboid," replied the student.

The teacher handed out worksheets and cuboid shaped packaging boxes to each group of students. They opened up the packing boxes so that their nets were laid flat and pasted them onto sheets of cardboard. Then the students gave each rectangular shaped face a number and wrote different letters next to the edges of the net according to how long they were (length [l], width [w], and height [h]) as shown below in the picture.

The area of each rectangular face was calculated. After finding the areas for all the faces the students  combined all the formulae and simplified them into a formula for finding the total surface area of the cuboid, which was 2 (lw + lh + wh).

Then the teacher invited two student representatives from one of the groups to present their results. It turned out that the other groups had the same answer, so the teacher continued to the next stage, namely asking the students to find the surface area of   a cuboid with a length of 12 cm, width of 8 cm and height of 6 cm.

By using the formula that they had found together, the students performed calculations as follows:

The surface area of a cuboid

= 2 (lw + lh + wh)
= 2 (96 + 72 + 48)
= 432 cm2

The teacher then gave them the two problems that were related to things that can be encountered in everyday life.

The first question was this: "Nesti wants to wrap a cuboid-shaped gift box (dimensions: length 25 cm, width 12 cm, height 10 cm) with wrapping paper. What is the minimum amount of   wrapping paper that Nesti requires to wrap the box?"

The second question was this: "A carpenter will make a cuboid-shaped closet that has been ordered by a customer. Its length, width and height will be 1 m, 0.5 m and 2 m, respectively. If the wood costs IDR 200,000  per m2, the varnish costs IDR 150,000 per m2, the accessories cost IDR 100,000, and labor costs IDR 500,000, what will be the selling price of this cabinet?"

The teacher went around the classroom to assist the groups as they worked and asked and answered questions with the students. "The amount of wood required can be calculated based on the surface area. Does any one know it?" asked the teacher. "It is 7m2," answered one student.

"Well, the wood costs IDR 200,000 per meter. So how much will the required wood cost?” asked the teacher. "It is 7 x 200,000, sir," replied a student. "The cabinet will be coated with varnish for which the cost is IDR 150,000 per m2. How much area of wood needs to be varnished? It is 7m2. So the cost of varnish for 1 m2 is multiplied by 7, and then added to the other costs. So we can find the cost of making the closet," said the teacher again.

Then, representatives of the groups presented their work. For the first question, the students found that the surface area of   the gift box was 1,340 cm2. Here are the results of their calculations:

= 2 (lw + lh + wh)
= 2 {(25 x 12) + (25 x 10) + (12x10)}
= 2 (300 + 250 + 120)
= 600 + 500 + 240
= 1,340 cm2

As for the second question, the students found that the selling price for the closet is IDR 3,050,000. Here are the results of the calculations done by the student to find the cost of making the closet:

2 (lw + lh + wh) = 2 {(1x1 / 2) + (1x2) + (2.1 / 2)}
= 2 (0.5 + 2 + 1)
= 7m2

The selling price of the closet = (surface area x cost of wood) + (surface area x varnish) + accessories + labor

= (200,000 x 7) + (150.000 x 7) +100,000 + 500,000
Total = IDR 3,050,000

"So, you are able to calculate the cost of making a closet. And it's not just about making that closet because there are a lot of other occasions where you need to use the formula to find the surface area of a cuboid," said Akidin. The lesson finished with a reflection activity. (Tif/Anl)


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