The difference be

Given:

R – r = 7 cm

A – a = 1078 cm²

Where,

R = radii of the larger circle

r = radii of the smaller circle

A = area of the larger circle

a = area of the larger circle

A = πR²

And,

a = πr²

∵ R – r = 7

⇒ R = 7 + r

Now,

A – a = πR² – πr² = 1078

⇒ πR² – πr² = 1078

⇒ π(7 + r)² – πr² = 1078

⇒ π[(7 + r)² – r²] = 1078

⇒ π[(49 + r² +14r – r²] = 1078

⇒ 3.14[(49 + r² +14r – r²] = 1078

⇒ 3.14(49 + 14r) = 1078

⇒ 3.14(49 + 14r) = 1078

⇒ 3.14 × 7(7 + 2r) = 1078

⇒ 7 + 2r = 49

⇒ 2r = 49 – 7

⇒ 2r = 42

Hence, radius of smaller circle = 21 cm