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# A cone is formed by bending a sector of a circle having an angle of 210o. Find t...

### Question

A cone is formed by bending a sector of a circle having an angle of 210o. Find the radius of the base of the cone if the diameter of the circle is 12cm.

### Options

A) 12cm

B) 7.00cm

C) 1.75cm

D) 21cm

E) 3.50cm

The correct answer is E.

### Explanation:

If diameter of the circle = 12cm; radius of the circle(L) = $$\frac{12}{2}$$
= 6cm
$$\frac{\theta}{360}$$ = $$\frac{r}{L}$$ where $$\theta$$ = 210$$^{\circ}$$, L = 6cm
$$\frac{210}{360}$$ = $$\frac{r}{6}$$
where r = radius of the base of the cone
V = $$\frac{1260}{360}$$
= 3.50cm

## Dicussion (1)

• If diameter of the circle = 12cm; radius of the circle(L) = $$\frac{12}{2}$$
= 6cm
$$\frac{\theta}{360}$$ = $$\frac{r}{L}$$ where $$\theta$$ = 210$$^{\circ}$$, L = 6cm
$$\frac{210}{360}$$ = $$\frac{r}{6}$$
where r = radius of the base of the cone
V = $$\frac{1260}{360}$$
= 3.50cm