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Gekata
13 days ago
12

(Pic above) In the figure above , O is the center of square. What is the area of the square?

Mathematics
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If the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change
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Answer:

  (1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

  s = ∛V

and the surface area is given by...

  A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

  r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

  r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

  r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

___

Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

<pif we="" multiply="" the="" edge="" length="" by="" new="" volume="" equals="" and="" surface="" area="" equates="" to="" so="" area-to-volume="" ratio="" becomes...="">

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

</pif>
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2 months ago
the moon is about 240,000 miles from earth .What is the distance written as a whole number multiplied by a power of ten?
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The distance to the moon is approximately 240,000 miles. This can be expressed as 2.4 multiplied by 10 raised to the power of 5.
8 0
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Read 2 more answers
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