a cube with 2 in sides is placed on a cube with 3 in sides. then a cube with 1 in sides is placed on the 2 in cube. what is the surface area of the three cube tower?
5 sides of the top cube is exposed.
so we get 1*1 * 5 = 5 in ^2
the second cube has 4 sides exposed also, so 2^2 * 4 = 16 in ^2, but also it has one side with the cube on top, so we have 4-1 = 3 on that side, so the overall is 19 in ^2
Then we have for the third cube 5 sides exposed, so we have 3^2 * 5 = 45. We also have the area of the 2in cube on it, so we get 3^2 - 2^2 = 9-4 =5.
So the overall is 45+5+19+5 = 55+19 =74 if i am not mistaken...
74
Yes, that is correct! The surface area of the three cube tower is 74 square inches.
Well, that's a tall tower of cubes you've got there! Let's calculate the surface area step by step:
The large cube with sides of 3 inches has a total surface area of 6 * (3 in)^2 = 54 square inches.
Next, we have the medium-sized cube with sides of 2 inches. Since we only have one on top, we need to calculate only five of its faces. Therefore, the surface area is 5 * (2 in)^2 = 20 square inches.
Finally, we have the tiny cube with sides of 1 inch. Again, since we only have one on top, we need to calculate only five of its faces. So, the surface area is 5 * (1 in)^2 = 5 square inches.
Now, to find the total surface area of the three-cube tower, we just need to add up all the individual surface areas: 54 + 20 + 5 = 79 square inches.
So, the surface area of the three-cube tower is 79 square inches. Enjoy your tower of cubes, and may it reach great heights (pun intended)!
To find the surface area of the three-cube tower, we need to find the surface area of each cube and add them together.
Let's start with the largest cube, which has sides of length 3 inches. The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying the result by 6 (since there are 6 faces on a cube).
Surface area of the 3-inch cube:
Side length = 3 inches
Surface area = 3 * 3 * 6 = 54 square inches
Next, let's move to the middle cube, which has sides of length 2 inches. We follow the same process:
Surface area of the 2-inch cube:
Side length = 2 inches
Surface area = 2 * 2 * 6 = 24 square inches
Finally, let's calculate the surface area of the smallest cube, with sides of length 1 inch:
Surface area of the 1-inch cube:
Side length = 1 inch
Surface area = 1 * 1 * 6 = 6 square inches
Now, we can find the total surface area of the three-cube tower by adding up the surface areas of each cube:
Total surface area = Surface area of the 3-inch cube + Surface area of the 2-inch cube + Surface area of the 1-inch cube
Total surface area = 54 square inches + 24 square inches + 6 square inches
Total surface area = 84 square inches
Therefore, the surface area of the three-cube tower is 84 square inches.