Question

If the circumference of a circle is increased by 50%, then its area will be increased by (a) 100% (b) 125% (c) 150% (d) 75%​

Answer 1

Answer:

Hi, There!

Option B 125% Is the Most Accurate Answer

Step-by-step explanation:

Circumference is the distance around a plane shape. So, it also measures length.

Length and area of two similar shapes are related by the formula

$\frac{A_{1} }{A_{2} } =(_{} \frac{I_{1} }{I_{2\\ ^{~2~} }}$

Where the A in both cases represents area and the L represents length. But here the Ls will represent circumference.  

Since the circumference of the circle increased by 50%, then the new circumference becomes

$l_{2} = l_{1} + 0.5l_{1} =1.5l_{1}$

Now subtracting from the original area then  

$2.25 - 1=1.25$

This means that the area was increased by 1.25, which means 125%

 

Hence option B is the correct answer