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The surface area S of a cube with volume V is S = 6V 2/3. What effect does increasing the volume have f a cube by a factor of 7 have on the surface area?

User Smashbro
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Final answer:

Increasing the volume of a cube by a factor of 7 increases its surface area by 7^(2/3) times, which is less than a factor of 7 because the surface area increases at a slower rate than the volume.

Step-by-step explanation:

The question asks about the effect of increasing the volume of a cube by a factor of 7 on its surface area. We are given that the surface area S of a cube with volume V is S = 6V^(2/3). To find the new surface area after increasing the volume by a factor of 7, we plug in 7V in place of V into the formula. The new surface area S' will then be S' = 6(7V)^(2/3).

When evaluating this, we can simplify as follows:

  • S' = 6(7^(2/3) * V^(2/3))
  • S' = 6 * 7^(2/3) * V^(2/3)
  • S' = 6V^(2/3) * 7^(2/3)
  • S' = S * 7^(2/3) since S = 6V^(2/3)

The new surface area is 7^(2/3) times the original surface area, which is an increase, but by less than a factor of 7. This is because the surface area of a cube increases at a slower rate (V^(2/3)) compared to the volume increase (V).

User Liya
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