CAT 2017 Question Paper | Quants Slot 1

CAT Questions

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

---

---

Video Explanation

---

---

Explanatory Answer

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.