CAT 2017 Geometry & Mensuration Question (Medium)

Question

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

Accepted Answer

Step 1 Let the volumes of the five smaller cubes be x 3, x 3, 8x 3, 27x 3, 27x 3 Total volume of the original cube x 3 x 3 8x 3 27x 3 27x 3 64x 3 So, side of the original cube sqrt 3 64x 3 4x Step 2 Surface area of a cube Surface area of original cube 6 4x 2 6 cdot 16x 2 96x 2 Step 3 Sides of smalle

CAT 2017

Quantitative

Geometry & Mensuration

Medium

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 :

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