Question 12

Seven equal solid metallic spheres having radius $$6\ \text{cm}$$ are melted to cast a cuboid with length $$33\ \text{cm}$$ and width $$24\ \text{cm}$$. What will be the height of the cuboid so formed? (Use $$\pi = \frac{22}{7}$$)

Solution

The total volume of the spheres is $$7 \times \frac{4}{3} \times \frac{22}{7} \times 6^3 = 4 \times 22 \times 72 = 6336\ \text{cm}^3$$. This equals the cuboid's volume $$33 \times 24 \times h = 792h$$. So $$h = \frac{6336}{792} = 8\ \text{cm}$$.

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