Question

If the diameter of a circle in increased by 200%, by what percent will its circumference will increase?

Answer 1

Answer:

If the diameter of a circle in increased by 200%, its circumference will increased by 200%

Step-by-step explanation:

Let the diameter of circle be x.

Given diameter of a circle in increased by 200% then new diameter will be

$x+\frac{200}{100}x=x+2x=3x$

Circumference of circle = $2 \pi r=\pi \times D$

Circumference of original circle=$\pi \times x$

Circumference of new circle=$\pi \times 3x$

= 3 times Circumference of original circle

$\text{Percentage increase in Circumference} =\frac{\text{New circumference-original Circumference}}{\text{original circumference}} \times 100$            

$\text{Percentage increase in Circumference}={\frac{3x\pi-{x\pi}}{x\pi}\times 100$

$\text{Percentage increase in Circumference}={\frac{2x\pi}{x\pi}\times 100$    

$\text{Percentage increase in Circumference}=200$                        

Thus, If the diameter of a circle in increased by 200%, its circumference will increased by 200%