A hollow spherical shell is made of a metal of density 3 g/cm³. Its internal and external radius are 15 cm and 18 cm, respectively. What is the weight (in kg) of the shell ?
(take π=22/7)

Correct option is A

Given:

Density of metal = 3 g/cm³

Internal radius (r) = 15 cm

External radius (R) = 18 cm

​$$π= \frac{22}{7}$$​​

Formula Used:

Volume of a sphere = V = $$\frac{4}{3} \pi r^3$$​​

Volume of the hollow shell = $$V_{\text{shell}} = \frac{4}{3} \pi (R^3 - r^3)$$​​

Mass of the shell = $$\text{Density} \times \text{Volume}$$​​

Solution:

Putting the values in the formula;

​$$V_{\text{shell}} = \frac{4}{3} \pi (18^3 - 15^3)$$

​​$$V_{\text{shell}} = \frac{4}{3} \pi (5832 - 3325)$$​​

​​$$V_{\text{shell}} = \frac{4}{3} \times \frac{22}{7} \times 2457$$ = 10296 cubic cm

​$$\text{Mass} = 3 \times 10296 = 30888 \text{ g}$$ 

In 1 kg = 1000 g
1 g = $$\frac{1}{1000} kg$$  
​$$30888 \text{ g} = 30.888 \text{ kg}​$$​​