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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

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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