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Radius of quadrant of circle, R = 8.4cm
Perimeter of quadrant =  \frac{2 \pi R}{4} =  \frac{ \pi \times 8.4}{2}=4.2 \pi

Perimeter of quadrant = Perimeter of base of cone
let radius of cone = r
2 \pi r=4.2 \pi \\ \\ r= \frac{4.2 \pi }{2 \pi } =2.1\ cm
Slant height of cone is R, so slant height is 8.4cm.

R(circle Radius)=8.4
slant height(l)=R=8.4 cm
r(cone's radius)
x=(angle) 360/4=90

 \frac{r}{L} = \frac{x}{360}
 \frac{r}{8.4} = \frac{90}{360}  \\ 
  \\ \frac{r}{8.4}= \frac{1}{4} 
 \\  \\ 8.4=4r
 \\ r=8.4/4=2.1 cm

radius of the cone=2.1cm