Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
The percentage increase in the surface area of a cube when each side is increase
The percentage increase in the surface area of a cube when each side is increased to \( \frac{3}{2} \) times the original length is
- A. 225
- B. 200
- C. 175
- D. 125
Step-by-step solution
Let original side = s. Surface area = 6s². New side = (3/2)s. New surface area = 6*(3/2 s)² = 6*(9/4)s² = (27/2)s². Increase = (27/2 - 6)s² = (15/2)s². Percentage increase = ((15/2)/6)*100 = (15/12)*100 = (5/4)*100 = 125%.
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