Math, asked by wasbuttwb, 1 year ago

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

Answered by dvitibafna
3

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

Answered by eudora
9

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 = \frac{\text{Volume of big cube}}{\text{Volume of the smaller cubes formed}}

                                 = \frac{1^{3}}{(0.1)^{3}}

                                 = \frac{1}{0.001}

                                 = 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

= \frac{6}{60}

= \frac{1}{10}

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

Similar questions