The question is from CAT Percentages. CAT tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This questions combines a bit of Geometry with Percentage. Percentages is an important topic for CAT. When the length, breadth and height of a cube changes by some percentage, what will be percentage change in surface area of the cube?

Question 26: A solid cube made of steel is melted and recast such that its length, breadth and height changes as +10%, +10%, -20%. What is the percentage change in surface area of this cube?

- No Change
- +1%
- +2%
- -1%

–1%

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Let the surface area of each side of initial cube be 100.

The surface area of the resulting cuboid would be given by 2(lb + bh + lh)

So, ∆lb = 100 + 10% ---> 110 + 10% ---> 121

∆bh = 100 + 10% ---> 110 - 20% ---> 88

∆lh = 100 + 10% ---> 110 - 20% ---> 88

Therefore, new surface area = 2 (121 + 88 + 88) = 594

% change in surface area = a * (−6/600) ∗ 100 = −1 (Initial surface area = 6 sides x 100 = 600)

The question is **"What is the percentage change in surface area of this cube?"**

The percentage change in surface area of this cube is -1%.

Choice D is the correct answer.

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com