Question : The difference between the circumference and diameter of a circle is 150 m. The radius of that circle is:
Option 1: 25 m
Option 2: 35 m
Option 3: 30 m
Option 4: 40 m
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Correct Answer: 35 m
Solution :
Given: The difference between the circumference and diameter of a circle is 150 m.
Let the radius of the circle be $r$.
Its diameter = $2r$ and its circumference is $2\pi r$.
According to the question,
$2\pi r\ –\ 2r=150$
⇒ $2r(\frac{22}{7}-1)=150$
⇒ $r\times(\frac{22-7}{7})=\frac{150}{2}$
⇒ $r\times(\frac{15}{7})=75$
$\therefore r=35$ m
Hence, the correct answer is 35 m.
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