Question

If the diameter of a circle changes from 5 cm to 15 cm, how will the circumference change? A) multiplies by 1 3 B) multiplies by 3 C) increases by 10 D) decreases by 10

Answer 1

The length of a circumference: l=πD
l₁=π×5=5π
l₂=π×15=15π
Then l₂÷l₁=15π÷5π=3 and the answer is B)

Answer 2

Given that diameter of the old circle = 5 cm

Given that diameter of the new circle = 15 cm

Now we have to find the change in circumference from old to new circle.

To find that we need formula of circumference of the circle which is

circumference = D \pi

where D represents diameter of the circle.

Then ratio of the circumference of the both circle is given by

$\frac{Circumference_{old}}{Circumference_{new}}=\frac{D_{old} \pi}{D_{new} \pi}$

$\frac{Circumference_{old}}{Circumference_{new}}=\frac{5 \pi}{15 \pi}$

$\frac{Circumference_{old}}{Circumference_{new}}=\frac{1}{3 }$

That means circumference of the new circle is 3 times more than old circle.

Hence choice "B) multiplies by 3" is correct.