A large solid cube is melted and cast into 'N' small solid spheres, each of radius 3 cm, and N + 2' small solid cuboids, each of dimensions 4 cm × 4 cm × 6.5 cm. If the length of each side of the large solid cube is 12 cm, then find the value of 'N'.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 7
The volume of a large solid cube = N × volume of small solid spheres + (N + 2) × volume
of small solid cuboid
side³ = N × 4/3 x π x radius³ + (N +2) × length × breadth × height
123 = N × 4/3 × 22 x 33 + (N +2) × 4 × 4 × 6.5
1728 = N x 4 × 22/7 x 32+ (N+2) × 104
1728 N × 88/7 × 9 + (N + 2) × 104
864 = N × 44/7 × 9 + (N +2) × 52
864 = N × 396/7 + 52 N + 104
864 -104= (396N + 364N)/7
760 = 760N/7
N = 7