Question

A cone made of cardboard has a vertical height of $8cm$ and a radius of $6cm$. If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector?

• A. ${216}^o$
• B. ${180}^o$
• C. ${90}^o$
• D. ${36}^o$

Answer 1

The correct option is A ${216}^o$

Given $h=8cm,r=6cm$

WKT
$l^2=h^2+r^2$

$⟹l=\sqrt{64+36}=10$

Slant height $=10cm$

Circumference of base = $2\pi \times 6=12\pi cm$

Now, the cone is cut as shown and laid out flat on the floor to ge ta sector of radius = $l$ and arc length = $12\pi cm$

$⟹\theta =\frac{12\pi }{10}={216}^{\circ }$