Two solid spheres made of the same metal have weights 5920 g and 740 g. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Step-by-step solution

Idea: For the same material, weight is proportional to volume. Volume of a sphere is 43πr³, so the ratio of volumes is the cube of the ratio of radii.

1. Same metal ⇒ weight of largerweight of smaller = volume of largervolume of smaller = 5920740 = 8.1 mark
2. (4/3)πR³(4/3)πr³ = 8 ⇒ (Rr)³ = 8 ⇒ Rr = 2.1 mark
3. Smaller radius r = 5 ÷ 2 = 2.5 cm, so R = 2 × 2.5 = 5 cm.1 mark

Check: Radius 5 vs 2.5: volumes in ratio 5³ : 2.5³ = 125 : 15.625 = 8 : 1, and 740 × 8 = 5920 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Taking the radius ratio as 8 (forgetting the cube root).
• Using 5 cm as the smaller radius (it is the diameter), giving 10 cm.

How this can come in the exam

Try one yourself

Two iron balls weigh 1 kg and 64 g. The smaller has radius 1.5 cm. Find the radius of the larger.

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