Question : The outer radius of a spherical shell is 13 cm and the thickness of the shell is 3 cm. What is the volume of the metal used for the shell? $\left(\pi=\frac{22}{7}\right)$
Option 1: 1197 cm3
Option 2: 2197 cm3
Option 3: 3024 cm3
Option 4: 5016 cm3
Correct Answer: 5016 cm 3
Solution :
The outer radius of a spherical shell, $R$ = 13 cm
The thickness of the shell = 3 cm
The inner radius of a spherical shell, $r$ = 13 – 3 = 10 cm
The volume of the metal used for the shell = $\frac{4}{3} \pi (R^3-r^3)$
= $\frac{4}{3} × \frac{22}{7}× (13^3-10^3)$
= $\frac{4×22}{3×7} × (13-10)(13^2+10^2+13×10)$
= $\frac{88}{21} × 3 × (169+100+130)$
= $\frac{88}{7} × 399$
= 88 × 57
= 5016 cm
3
Hence the correct answer is 5016 cm
3
.
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