Question : 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'. [Use $\left.\pi=\frac{22}{7}\right]$
Option 1: 8
Option 2: 5
Option 3: 7
Option 4: 6
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Correct Answer: 7
Solution : According to the question, Volume of cube = volume of N-solid spheres + Volume of (N + 2) small cuboids ⇒ $12 \times 12 \times 12 =[ N \times \frac{4}{3}\times\pi\times 3^3] + [(N + 2)(4 \times 4 \times 6.5)]$ ⇒ $1728 = 36N\pi + 104N + 208$ ⇒ $1520 = N(36 \times\frac{22}{7} + 104)$ ⇒ $1520 = \frac{1520}{7}N$ ⇒ $N = 7$ Hence, the correct answer is 7.
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