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A cone is formed by bending a sector of a circle having an angle of...

Mathematics
JAMB 1984

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.
  • A. 12cm
  • B. 7.00cm
  • C. 1.75cm
  • D. 21cm
  • E. 3.50cm
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Correct Answer: Option 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\(\theta\), 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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