A hollow spherical shell is made of a metal of density 9 g/cm³. Its internal and external radius are 10 cm and 13 cm, respectively. What is the weight (in kg) of the shell ?
​$$(take \pi = \frac{22}{7})$$​

Correct option is A

Given:

Density of metal = 9$$\, \text{g/cm}^3.$$​​

Internal radius r = 10 cm

External radius R=13 cm

Formula Used:

Volume of spherical shell:

V =$$\frac{4}{3}\pi \left(R^3 - r^3\right)$$​

Mass = Density × Volume.

Solution:

Volume:

$$V = \frac{4}{3}\times \frac {22}7 \left(13^3 - 10^3\right) \\ \ \\V= \frac{4}{3}\times \frac {22}7 \times (2197- 1000)\\ \ \\V = \frac{4}{3} \times \frac{22}{7} \times 1197\\ \ \\V = \frac{22}{7} \times 1596 = \frac{35112}{7} = 5016 \, \text{cm}^3$$​

Mass (in g):

M = 5$$016 \times 9 = 45144 \, \text{g} =$$​45.144 kg