Question

What would be the side of a cube if the ratio of its volume to surface area is 1 : 1​

Answer 1

Answer:

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Step-by-step explanation:

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}}Volume of the smaller cubes formedVolume of big cube

                                 = \frac{1^{3}}{(0.1)^{3}}(0.1)313

                                 = \frac{1}{0.001}0.0011

                                 = 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}606

= \frac{1}{10}101

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

Answer 2

Answer:

Side of the cube is 6 units.

Step-by-step explanation:

Firstly, the formula for volume of a cube is (side)³ and formula for surface area is 6(side)².

Let the side of the cube is 'a'.

Now, the ratio of volume and surface area of cube is 1 : 1 (given)

i. e. Volume of cube / Surface area of cube = 1

(side)³/6 (side)² = 1

a³/6 a² = 1

a³ = 6 a²

a = 6

So, side of the cube is 6 units.