Question
A hollow spherical shell is made of a metal of density 39 g/cm3. Its internal and external radii are 12 cm and 13 cm, respectively. What is the weight (in kg) of the shell? (Use \(\pi = \frac{22}{7}\) and Density = Mass/Volume)
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RRB NTPC 2025 Under Graduate CBT 1 Question Paper PDF (20-Jun-2026) (Shift 3)
The correct answer is
76.648
The volume of the material of a hollow spherical shell with external radius \(R\) and internal radius \(r\) is \(V = \frac{4}{3}\pi (R^3 - r^3)\).
Here \(R = 13\) cm and \(r = 12\) cm, so \(R^3 - r^3 = 2197 - 1728 = 469\).
\(V = \frac{4}{3} \times \frac{22}{7} \times 469 = 1965.33\) cm3 (approximately).
Since Density \(= \frac{Mass}{Volume}\), Mass \(= Density \times Volume = 39 \times 1965.33 = 76648\) g.
Converting to kilograms: \(\frac{76648}{1000} = 76.648\) kg.
Hence, the weight of the shell is 76.648 kg.
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