Cubes

One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 257 mm².

Correct answer:

V₁-V₂ =  512.6 mm³

Step-by-step explanation:

$$\begin{gathered} S_1-S_2=6a_1^2-6a_2^2=6((2r{)}^2-(\sqrt{2}r{)}^2)=12r^2=257 \\ r=\sqrt{{\displaystyle \frac{257}{12}}}\doteq 5mm \\ {V}_1-V_2=a_1^3-a_2^3=(2r{)}^3-(\sqrt{2}r{)}^3=512.6{\text{mm}}^3 \end{gathered}$$

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Showing 2 comments:

Math student

What do all those symbols mean? Is there a more simple format...that you could put this in?

5 years ago  Like

Petr

S - surface area of cube
V - volume of cube(s)
r - radius of sphere

5 years ago  Like

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