Question

a quadrant of a circle of radius 8.4 cm is changed as cone. find radius and slant height of cone.

Answer 1

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.

Answer 2

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

$\frac{r}{L} = \frac{x}{360}$
[tex] \frac{r}{8.4} = \frac{90}{360} \\ \\ \frac{r}{8.4}= \frac{1}{4} \\ \\ 8.4=4r \\ r=8.4/4=2.1 cm [/tex]
radius of the cone=2.1cm