Question

what is the least number of solid metallic spheres,each of 6cm diameter, that should be melted and recasted to form a solid metal cone whose height is 45cm and diameter 12cm​

Answer 1

number of sphere × volume of sphere = volume of cone

$x \times \frac{4}{3} \pi {r}^{3} = \pi {r}^{2} \frac{h}{3} \\ x \times \frac{4}{3} \times 3 \times 3 \times 3 = 6 \times 6 \times \frac{45}{3} \\ x \times 4 \times 3 \times 3 = 6 \times 6 \times 15 \\ x = \frac{6 \times 6 \times 15}{4 \times 3 \times 3} \\ x = 15$

number of spheres required is 15

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