A solid metallic sphere of radius 4 cm weighs 4 kg. A hollow spherical shell of the same metal has outer diameter 16 cm and inner diameter 12 cm. Find the weight (in kg) of the hollow sphere.

Introduction / Context:
For the same material, weight is proportional to volume (same density). We can find the density from the solid sphere, then multiply by the shell volume to get the new weight.

Given Data / Assumptions:

• Solid sphere: radius 4 cm, weight 4 kg.
• Hollow sphere: outer radius R = 8 cm, inner radius r = 6 cm.
• Sphere volume: V = (4/3)πr^3.

Concept / Approach:
Density k = weight / volume for the first sphere. Then shell volume V_shell = (4/3)π(R^3 − r^3). Multiply k * V_shell for the new weight.

Step-by-Step Solution:

Verification / Alternative check:
Units cancel; π cancels; exact fractional arithmetic yields 18.5 kg.

Why Other Options Are Wrong:

• 20.5, 16.5, 15.5 kg: Do not match the exact shell volume times density.

Common Pitfalls:
Using surface area instead of volume; forgetting to convert diameters to radii; arithmetic slips in cube values.

Final Answer:
18.5 kg