How do I convert cubic picometer to cubic centimeter?

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To convert cubic picometers to cubic centimeters, the volume of a unit cell with a cell edge of 288 pm can be calculated by cubing the edge length in centimeters. The calculation involves converting 288 picometers to centimeters, resulting in 288 x 10^-10 cm. When cubed, this equals approximately 2.39 x 10^-23 cm^3. The detailed steps include using scientific notation and breaking down the calculations for clarity. Understanding this conversion is essential for accurate measurements in nanotechnology and materials science.
Rajdeep Biswas
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moved into the homework section, therefore no template shown
Part of the question says: An unit cell has a cell edge of 288 pm.
I got to the part where volume (288 pm)^3 = (288 x 10^-10 cm)^3
I have no idea how that equals 2.39 x 10^-23 cm^3

Only the Bold part ^
 
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##288^3=2.39 \cdot 10^{7}##
 
Rajdeep Biswas said:
... (288 x 10^-10 cm)^3
I have no idea how that equals 2.39 x 10^-23 cm^3

I'm a little confused. Plug 288x10^-10 into your calculator and hit the cubed button. If you would like to do it in your head try

(288e-10)^3 = (2.88e-8)^3
= 2.88^3 x (10^-8)^3
= 2.88^3 x 10^-24
= (3-0.12)^3 x 10^-24
= (3^3 - 3*3^2*0.12 + small) x 10^-24
~= 27*(1-0.12) x 10^-24
~= (27-2.7-0.54) x 10^-24
= 2.376 x 10^-23
 
(288 * 10-10)3
= 2883 * (10-10)3
= 2.39 * 107 * 10-10 * 10-10 * 10-10
= 2.39 * 10-23
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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