a cuboid of size 8cm*4cm*2cm is cut into cubes of equal size of 1cm side. what is the ratio of the surface area of the original cuboid to the surface areas of all the unit cubes so formed?
Answers
Solution:
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
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
Answer:
Solution:
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=164=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}=384112=247