# CAT 2017 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Mensuration and Geometry Questions | Question 18

This qusetion is from Mensuration. Mensuration is a fairly intuitive topic in CAT Geometry. Other than knowing basic formulae, structural and spatial understanding of the shapes helps one nail Mensuration questions in the CAT exam. Mensuration comprises of 2D and 3D shapes including Spheres, Cubes, Cuboids, Cylinders, Cones and more. You can expect at least one question from Mensuration in CAT exam.

Question 18 : A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to :

1. 10
2. 50
3. 60
4. 20

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

##### Method of solving this CAT Question from Mensuration and Geometry

Given that a solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. We have to find the percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube.
Let us take the volume of the 5 cubes to be 1x3 , 1x3 , 8x3 , 27x3 , 27x3
Volume of the original cube = x3(1 + 1 + 8 + 27 + 27)
Volume of the original cube = 64x3
Sides of the original cube = ∛64x3 = 4x
Similarly, sides of the 5 smaller cubes = x , x , 2x , 3x , 3x .
Surface Area of a cube = 6a2
Surface Area of the original cube = (4x) × (4x) = 16x2
Surface area of the smaller cubes = x2 , x2 , 4x2 , 9x2 , 9x2
Sum of the surface areas of the smaller cubes = x2(1 + 1 + 4 + 9 + 9) = 24x2
Change in surface area = 24x2 – 16x2 = 8x2
%change = $$frac{8x^2}{16x^2}$ × 100 = 50% Hence the percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to 50%. The question is "A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to :" ##### Hence, the answer is 50% Choice B is the correct answer. ###### 🎉Get Upto ₹10,000 off on our CAT 23/24 courses.🎉Flat ₹6000 off on IPM courses. ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com