Question : The sum of the lengths of the radius and the diameter of a circle is 84 cm. What is the difference between the lengths of the circumference and the radius of this circle? [Use $\pi=\frac{22}{7}$]
Option 1: 156 cm
Option 2: 172 cm
Option 3: 148 cm
Option 4: 128 cm
Correct Answer: 148 cm
Solution :
Given: The sum of the lengths of the radius and the diameter of a circle is 84 cm.
Use the formula,
The diameter of the circle = $2r$,
The circumference of the circle = $2\pi r$,
where $r$ is the radius.
According to the question,
$r+2r=84$
⇒ $3r=84$
⇒ $r=28$ cm
The difference between the lengths of the circumference and the radius of this circle = $(2\times \frac{22}{7}\times 28)-28=176-28=148\ \text{cm}$
Hence, the correct answer is 148 cm.
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