a solid cube of side 12cm is cut into 8 identical cubes.what will be the side of the new cube?also find the ratio between the surface area of the origional cube and the total surface area of all the small cubes formed.
Answers
Answer:
1:2 ?
Step-by-step explanation:
volume of original cube=12*12*12=1728 cm^3. therefore volume of smaller cubes=216 cm^3.
so, length of side of smaller cube = cube root of 216 = 6 cm. surface area of original cube = 6a^2=6*12*12=864 cm^2. surface area of one of the smaller cubes=6*6*6=216 cm^2. therefore total surface area of all the smaller cubes = 8*216 = 1728 cm^2. hence ratio of surface areas = 864 / 1728 = 1/2
Answer:
Side of each of the new cube = 6 cm
Ratio between TSA of original cube and TSA of all the new cubes formed = 1 : 2
Step-by-step explanation:
The total volume of the 8 cubes will be equal to the volume of the original cube.
Let the side of the new cubes be S.
Hence,
8 × S^3 = 12^3
S^3 = 12^3 / 8
S^3 = (12 / 2)^3
S^3= 6^3
S = 6 cm
Since surface area of a cube = 6 × (side)^2,
Surface area of each of the new cube = 6 × (6)^2 = 6 × 36 = 216 cm^2
Hence, surface area of all the cubes :
8 × 216 = 1728 cm^2
Surface area of the original cube :
6 × (12)^2 = 6 × 144 = 864 cm^2
Hence,
Ratio = 864 : 1728 = 1 : 2