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Sally has a cube of side length  units such that the number of square units in the surface area of the cube equals 1/10 of the number of cubic units in the volume. She also wants to make a square for which the number of square units in the area of the square is equal to the number of cubic units in the volume of the cube. What should the side length of the square be?

 Nov 8, 2020
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Sally has a cube of side length  units such that the number of square units in the surface area of the cube equals 1/10 of the number of cubic units in the volume. (condition1)

She also wants to make a square for which the number of square units in the area of the square is equal to the number of cubic units in the volume of the cube. (condition2)

What should the side length of the square be?

 

Hello Sally!

 

condition1

\(\color{blue}6a^2=\frac{1}{10}a^3\\ a^3-60a^2=0\\ a^2(a-60=0) \)

\(a=60\)      

 

The cube has a side length of 60 side length units.

 

condition2

\(x^2=y^3\)

\(2log(x)=3log(y)\\ log(y)=\frac{2}{3}log(x)\\ {\color{blue}y=10^{\frac{2}{3}log(x)}}\ |\ \{x,y\} \subset \mathbb N\)

 

x : 1, 8, 64, 1000 \( side\ length\ units\)     square

y : 1, 4, 16,   100 \( side\ length\ units\)     cube

 

The side length of the square is \(\{1, 8, 64, 1000\}\ side\ length\ units.\)

 

Condition1 and condition2 are not compatible.

 Nov 10, 2020
edited by asinus  Nov 10, 2020

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