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Grade 7 POTW: How I did this was to figure out both the surface area of the original cube and the cube that was cut.
ORIGINAL CUBE: Since the question states only the side lengths, I would have to figure out one surface of the cube first. 10*10 = 100 cm squared. This is one surface of the cube, but since it is a cube all faces are equal. Therefore, 100*6=600 cm squared. I multiplied by 6 since there are 6 sides on a cube.
This would be the surface area of the original cube. Now, onto the smaller ones!
SMALLER CUBES: Since there were 3 cuts made and 8 identical cubes, it would mean that each time the cube was cut into halves three times. This would create 8 cubes.
Thus, the side length of a small cube would be 10/2 = 5cm. Using what I did with the original cube, I first need to find the area of one surface of the cube. 5*5 = 25 cm squared Since there are 6 sides, I multiply 25 by 6. 25*6 = 150. This is the surface area of one small cube, but there are still 7 others!
Thus, I multiply 150 by 8, which gives me 1200 cm squared in total.
The difference is 1200 - 600 = 600 cm squared.
Conclusion: The difference in surface area between the large cube and the 8 smaller cubes is 600 cm squared.
There is actually another way to solve this as well. Looking at the cube, the only difference between it being cut and not being cut are the sides between the small cubes. Those faces facing the inside of the cube are the extra. After figuring out that each side length of the small cube is 5 cm(Yes, that still has to be done) one surface would be 25 cm squared. Now, I counted the amount of extra faces there are, which in total is 24.
24*25 = 600 cm squared. That is the extra, being the same as my other strategy to solve the problem.
The formula for calculating the surface area of a cube is 6 (a squared), with a being the side length of one of the cube's sides. Since the side length of of one of the cube's sides is 10cm, we can plug that into the equation.
If a=10cm...
6(10cm squared) 6(100cm2) 600cm2
Therefore, the surface area of the original cube is 600cm2. Since the original cube's length, width and height are cut in half to make the smaller cubes, the side length of all of the small cubes would be 5cm. Next, I plugged that into the equation.
If a=5cm....
6(5cm squared) 6(25cm2) 150cm2
Therefore, the surface area of each of the small cubes is 150cm2. Since there are 8 cubes, the surface area of all of them is 1200cm2. In order to find the difference between the surface areas, I subtracted the surface area of the original cube from that of the smaller cubes.
1200cm2-600cm2=600cm2.
Therefore, the difference between the surface area of the cube shown and the smaller cubes is 600cm2.
Grade 7 POTW: Bigger cube= 10*10*10, surface area would be 10*10*6 because 10*10 would be the area of one face, and a cube has six identical faces. So the surface area is 600cm2. The smaller cubes would be 5*5*5, as the lines are cutting the cube in eight identical cubes. So we could simply do 5*5*6= 150. Since there are eight cubes, 150*8= 1200cm2. 1200-600=600cm2 difference. Sorry for another late POTW.
Grade 7 POTW:
ReplyDeleteHow I did this was to figure out both the surface area of the original cube and the cube that was cut.
ORIGINAL CUBE:
Since the question states only the side lengths, I would have to figure out one surface of the cube first.
10*10 = 100 cm squared.
This is one surface of the cube, but since it is a cube all faces are equal.
Therefore, 100*6=600 cm squared.
I multiplied by 6 since there are 6 sides on a cube.
This would be the surface area of the original cube. Now, onto the smaller ones!
SMALLER CUBES:
Since there were 3 cuts made and 8 identical cubes, it would mean that each time the cube was cut into halves three times. This would create 8 cubes.
Thus, the side length of a small cube would be 10/2 = 5cm.
Using what I did with the original cube, I first need to find the area of one surface of the cube.
5*5 = 25 cm squared
Since there are 6 sides, I multiply 25 by 6.
25*6 = 150.
This is the surface area of one small cube, but there are still 7 others!
Thus, I multiply 150 by 8, which gives me 1200 cm squared in total.
The difference is 1200 - 600 = 600 cm squared.
Conclusion: The difference in surface area between the large cube and the 8 smaller cubes is 600 cm squared.
There is actually another way to solve this as well.
Looking at the cube, the only difference between it being cut and not being cut are the sides between the small cubes. Those faces facing the inside of the cube are the extra. After figuring out that each side length of the small cube is 5 cm(Yes, that still has to be done) one surface would be 25 cm squared.
Now, I counted the amount of extra faces there are, which in total is 24.
24*25 = 600 cm squared.
That is the extra, being the same as my other strategy to solve the problem.
-Alan
Grade 7: Let's say X is 1 and Y is 2. It would be 2400 cm squared. But, you could really substitute X and Y for anything.
ReplyDeleteGrade 7 POTW:
ReplyDeleteThe formula for calculating the surface area of a cube is 6 (a squared), with a being the side length of one of the cube's sides. Since the side length of of one of the cube's sides is 10cm, we can plug that into the equation.
If a=10cm...
6(10cm squared)
6(100cm2)
600cm2
Therefore, the surface area of the original cube is 600cm2. Since the original cube's length, width and height are cut in half to make the smaller cubes, the side length of all of the small cubes would be 5cm. Next, I plugged that into the equation.
If a=5cm....
6(5cm squared)
6(25cm2)
150cm2
Therefore, the surface area of each of the small cubes is 150cm2. Since there are 8 cubes, the surface area of all of them is 1200cm2. In order to find the difference between the surface areas, I subtracted the surface area of the original cube from that of the smaller cubes.
1200cm2-600cm2=600cm2.
Therefore, the difference between the surface area of the cube shown and the smaller cubes is 600cm2.
Maxwell's Grade 7 POTW:
ReplyDeleteThe difference between the two surface areas of the larger cube and the smaller cubes is 600 cm squared. I did the math in my math notebook.
Grade 7 POTW:
ReplyDeleteBigger cube= 10*10*10, surface area would be 10*10*6 because 10*10 would be the area of one face, and a cube has six identical faces. So the surface area is 600cm2.
The smaller cubes would be 5*5*5, as the lines are cutting the cube in eight identical cubes. So we could simply do 5*5*6= 150. Since there are eight cubes, 150*8= 1200cm2. 1200-600=600cm2 difference. Sorry for another late POTW.
600cm2
ReplyDelete600cm2
ReplyDeleteI did it hard copy the answer is 450cm squared
ReplyDelete