Multiple choice

Maya owns a retail store where the dimensions of length, width, and height are in the ratio 6 : 4 : 3. She plans to expand the store by doubling the length and reducing both the width and height by one-third. By what percentage will the total surface area (T.S.A.) of the store change as a result of this expansion?

  1. Increase by 16.6%

  2. Increase by 13.6%

  3. Decrease by 13.6%

  4. Decrease by 16.6%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial dimensions: 6k, 4k, 3k. TSA = 2(24k^2 + 12k^2 + 18k^2) = 2(54k^2) = 108k^2. New dimensions: 12k, (2/3)*4k, (2/3)*3k = 12k, 8k/3, 2k. New TSA = 2((12k * 8k/3) + (8k/3 * 2k) + (12k * 2k)) = 2(32k^2 + 16k^2/3 + 24k^2) = 2(56k^2 + 5.33k^2) = 122.66k^2. Change = (122.66 - 108)/108 = 14.66/108 = 13.57%.

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