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
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32432)