Question

If the radius of a circle gets increased by 10%, then what is the percentage increase in its diameter?

• A. 40%
• B. 20%
• C. Remains same
• D. 10%

Answer 1

The correct option is D 10%

Let the radius of the circle be $r$.

We know that the diameter of a circle is twice its radius.

Hence, Daimeter $=2\times r=2r$

Now, increased radius $=\frac{110}{100}r=\frac{11}{10}r=1.1r$

$\Rightarrow$ Increased diameter $=2\times \frac{11}{10}r=\frac{22}{10}r=2.2r$

$\Rightarrow$ Increment iin diameter $=2.2r-2r=0.2r$

$\Rightarrow$ Percentage increment in diameter $=\frac{Incrementinthediameter}{Olddiameter}\times 100$

$=\frac{0.2r}{2r}\times 100=10$%

Thus, the diameter will also get increased by 10%.