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Which of the following percentages is the highest?
20%
16%
14%
23%
16%
Use the formula (1+100aтАЛ)(1+100bтАЛ)тИТ1 where a=+20 and b=тИТ30. Calculation: (1.20├Ч0.70)=0.84. Change = (0.84тИТ1)=тИТ0.16, which is a 16% decrease.
Radius r is increased by 20%, Height h is decreased by 30%
CSA=2├Ч╧А├Чr├Чh
Use the formula (1+100aтАЛ)(1+100bтАЛ)тИТ1 where a=+20 and b=тИТ30. Calculation: (1.20├Ч0.70)=0.84. Change = (0.84тИТ1)=тИТ0.16, which is a 16% decrease.
Students often mistakenly try to calculate the change in total surface area (2╧Аr(r+h)) or forget to treat the decrease as a negative percentage, leading to errors in the final sign.
Define Initial Variables
Let initial radius be r and initial height be h. The original curved surface area (CSA) is calculated as CSA1тАЛ=2╧Аrh.
CSA1тАЛ=2╧Аrh
Apply Percentage Changes
The radius increases by 20%, so rтА▓=r+0.20r=1.2r. The height decreases by 30%, so hтА▓=hтИТ0.30h=0.70h.
rтА▓=1.2r,hтА▓=0.7h
Calculate New CSA
Substitute new dimensions into the formula: CSA2тАЛ=2╧А(1.2r)(0.7h)=0.84├Ч(2╧Аrh).
CSA2тАЛ=0.84├ЧCSA1тАЛ
Determine Percentage Change
The percentage change is calculated as CSA1тАЛCSA2тАЛтИТCSA1тАЛтАЛ├Ч100=CSA1тАЛ0.84CSA1тАЛтИТCSA1тАЛтАЛ├Ч100=тИТ16%.
Percentage┬аChange=тИТ16%
B is correct because the final curved surface area is 84% of the initial area, representing a 16% decrease.
This ratio method works for all product-based formulas (e.g., volume of a cuboid, area of a rectangle) and is much faster than calculating exact surface area values.
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