An 8cm cube is cut into 2 cm cubes. Calculate the total surface area of all the small cubes
Answers
Answer:
Total surface area of cuboid of size 8 cm , 4 cm and 2 cm is given by the formula = 2 ×[LB+B H+H L]
Where, L=Length, B=Breadth, H=Height
=2 ×[ 8 ×4+4 ×2+8×2]
= 2 ×[32+8+16]
=2 ×56
=112 cm²
Volume of cuboid = L ×B×H
= 8 ×4×2
= 64 cm³
Volume of cube of side 1 cm = (Side)³=1³=1 cm³
So, number of cubes having volume 1 cm³ that can be cut from cuboid of volume 64 cm³ is given by =\frac{64}{1}=64=
1
64
=64
So, surface area of cube = 6(side)²=6 ×1×1=6 cm²
Surface area of 64 cubes each of side 1 cm = 64 ×6=384 cm²
Ratio of surface of original cuboid to the surface areas of all the unit cubes so formed =\frac{112}{384}=\frac{7}{24}=
384
112
=
24
7
Step-by-step explanation:
Total surface area of cube= 6a²
area of 4 small cubes = 8 cm
therefore TSA of cube =6 (8)²
=6*64
= 384 cm²
for single small cube
a=2 cm
TSA of cube=6 a²
=6*2²
=24 cm²