Answers

  • Brainly User
2016-01-24T03:03:05+08:00
ANSWER:  The total surface area of a cube increases by 77% if its edge is increased by 33%.

Surface Area = 6 (a)²       where a = edge

Example:  x = 4 units
   SA₁ = 6 (4)²
         = 6 (16)
         = 96 units²

If 4 units is increased by 33%:
   (Multiply 4 by 1.33  ⇒  5.32 units)
   SA₂ = 6 (5.32)²
         = 6 (28.30)
         = 169.80 units²

To find the rate of increase in total surface area (SA₂ - SA₁):
        =  \frac{169.80 - 96}{96}  \frac{73.8}{96}
   
        ≈ 0.76875  or 77%

If 5.32 units is increased by 33%:
   (Multiply 5.32 by 1.33  ⇒   7.08 units)
   SA₃= 6 (7.08)²
         = 6 (50.13)
         = 300.78 units²

To find the rate of increase in total surface area (SA₃ - SA₂):
         =  \frac{300.78 - 169.80}{169.80}  \frac{130.98}{169.80}
         ≈ 0.7713 or 77%

   
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