What is the ratio of the surface area of a cube with side 1 cm to the total surface area of the cubes formed by breaking the original cube into identical cubes of side 1 mm?
Answers
Answer:
1/10
Step-by-step explanation:
1 cm=10mm
Ratio of surface areas=
(6×10×10)/(10×10×10×6×1×1)
=600/6000= 1/10
Ratio of the total surface area of original cube and the cubes formed by breaking the original cube will be 1 : 10
Step-by-step explanation:
Total surface area of a cube is given by the formula
S = 6a²
Therefore, surface area of a cube with 1 cm = 6 cm²
If this cube is broken into small cubes of side = 1 mm or 0.1 cm then number of small cubes formed =
=
=
= 1000
Now surface area of 1000 smaller cubes = 1000(6)(0.1)²
= 60 cm²
Now the ratio of surface areas of original cube and smaller cubes formed will be
=
=
Therefore, ratio of the total surface area of the original cube and the smaller cubes will be 1 : 10
Learn the formulas of surface areas and volume of different structures from
https://brainly.in/question/8389124