Answer:
V(a) = 3,750mm^3
Step-by-step explanation:
for mathematically similar figures scale factor (sf) is common
that is if their lengths ratio is 3
then their areas ratio will be 3^2
volume's ratio will be 3^3
So here in this problem we have Surface Areas
by that we will find sf^2
SA(b) / SA(a) = 10478 / 1550 = 6.76
sf^2 = 6.76
sf = 2.6
now volumes ratio will be
V(b) = sf^3 * V(a)
= 2.6^3 * V(a)
= 17.576 * V(a)
Substitute this in the Volume equation given
V(b) - V(a) = 62160
=> 17.576 * V(a) - V(a) = 62160
=>16.576 * V(a) = 62160
=> V(a) = 62160 / 16.576
=> V(a) = 3,750
