How large will the Sun appear at 300mm on a Canon APS-C camera?

With your camera and existing 70-300 lens, shoot pictures of the moon. The moon and the Sun appear in the sky as a disk, they image exactly the same as to size. Both are 1/2 degree of arc disks.

Addendum: Figuring out the size of the Sun's image is easy math. You can trace out a triangle from the edges of the Sun to the camera lens. The image forming rays from the lens trace out a similar triangle inside the camera. Ratio to the rescue: Sun's diameter is 864,576 miles. Sun’s mean distance from Earth is 92,955,807 miles. The ratio diameter to distance is 92955807 ÷ 864576 = 0.00934.

The image forming rays of the camera lens trace out a triangle with this exact ratio. Thus if a 300mm lens is mounted, we multiply 300 X 0.00934 = 2.8. That tells us that if a 300mm lens is used, the image of the Sun at film or digital sensor will be a circle 2.8mm in diameter.

We view the images of our miniature cameras by making an enlargement, be it print on paper or image on a computer monitor. To make an 8X10 print from a full frame (FX), the magnification requires a minimum of 8.5X. If this is the magnification, the final image of the Sun will be 2.8 X 8.5 = 23.8mm (about 1 inch). If the camera is a compact (DX or APS-C), the magnification will be about 1.5X more - thus 23.8 X 1.5 = 35.7mm (Sun’s image diameter or about 1.4 inches).