Answer:
Let:
r= radius= 3cm= 0.03m
∅1= initial temperature= 30°C
∅2= final temperature= 100°C
∆∅= change in temperature= ∅2 - ∅1= 70°C
L.E.= linear expansivity= 0.000019k^-1
¥= 3L.E.= volume expansivity= 3(0.000019)= 0.000057k^-1
The initial volume of the metal sphere= 4/3(πr³)
= 4/3(π×0.03³)
= 4(π×0.03²×0.01)
= 4(3.142×0.0003×0.01)
= 4(0.000009426)
= 0.000037704
= 3.7704 × 10^-5m³
¥= V2 - V1/V1∆∅
V2= ¥V1∆∅ + V1
= (1.5044 × 10^-7) + (3.7704×10^-5)
= 0.00003785
= 3.785 × 10^-5m³
Therefore, the initial and final volume of the metre sphere are 3.7704 × 10^-5 and 3.785 × 10^-5 respectively.
