The answer you wrote for Q10(a)(i) should be correct.

For Q10(a)(ii), the arc length of the sector is equivalent to the circumference the circle when it was folded into a cone.

Circumference of circle is:
2 x 3.142 x 2.5 = 15.71 cm

Since the angle must be in radians,
s = rθ
15.71 = (11.5)(θ)
θ = 15.71/11.5 = 1.37 rad (3 s.f.)

For Q10(b),
Radius : Height = 1 : 3

Given that radius of sphere is 2.5 cm,
h = 2.5 x 3 = 7.5 cm

Volume of sphere is:
4/3 x 3.142 x 2.5³ = 65.45833...

Volume of cone:
1/3 x 3.142 x 2.5² x 7.5 = 49.09375

Since the volume of cone is smaller than the volume of sphere, it won’t fill the cone exactly and melted ice-cream will overflow.

The assumption that I could think of is: We’re assuming that there’s no change in volume when the ice-cream changes from solid to liquid state.

The limitation of solution could be (but I’m not sure): We don’t know the amount of ice-cream that has evaporated throughout the whole process.

Thank you

No problem.