Question 21

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Jambmaths question: 

A sector of circle of radius 7.2cm which subtends an angle of 300oat the centre is used to form a cone. What is the radius of the base of the cone? 

Option A: 

8cm

Option B: 

6cm

Option C: 

9cm

Option D: 

7cm

Jamb Maths Solution: 

$\begin{align}  & \text{Length of the arc}=x=\frac{\theta }{{{360}^{\text{o}}}}\times 2\pi l---(i) \\ & \text{Also }x\text{ is equal to the length of the perimeter of the } \\ & \text{circular base of the cone} \\ & x=2\pi r-----(ii) \\ & \therefore \frac{\theta }{{{360}^{\text{o}}}}\times 2\pi l=2\pi r;\text{      }\frac{\theta }{{{360}^{\text{o}}}}=\frac{r}{l} \\ & \frac{{{300}^{\text{o}}}}{{{360}^{\text{o}}}}=\frac{r}{7.2} \\ & r=\frac{{{300}^{o}}}{{{360}^{o}}}\times 7.2=6cm \\\end{align}$

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