The diagram represents a solid cone - Edexcel - GCSE Maths - Question 19 - 2020 - Paper 2

The formula for the curved surface area of a cone is given by:

$A = \pi r l$

where $r$ is the radius and $l$ is the slant height. For the entire cone:

$A = \pi \times 10 \times 25 = 250\pi \text{ cm}^2$

Using the same formula for the smaller cone with $r = 4$ cm and $l = 10$ cm:

$A_{small} = \pi \times 4 \times 10 = 40\pi \text{ cm}^2$

Subtracting the area of the smaller cone from the area of the entire cone:

$A_{not\, grey} = A - A_{small} = 250\pi - 40\pi = 210\pi \text{ cm}^2$

Therefore, the area of the curved surface of the cone that is not painted grey is:

$210\pi \text{ cm}^2$