Question

Martina has a circle with a diameter

of 6 inches. She doubled the
diameter to make a new circle.
Now, Martina says that the ratio of
the circle's circumference to its
diameter has also doubled. Correct
her mistake.

Answer 1

The ratio of the circumference to its diameter remains the same.

Explanation:

Given,

diameter of circle = 6 inch

diameter is doubled.

New diameter of circle = 2 x 6 = 12 inch

We know that,

The Circumference of a circle is 2 π r or π d where r is the radius of the circle and d is the diameter of the circle.

Circumference of the circle when the diameter is 6 inches.

C₁ = 6π

Ratio of circumference to diameter

Ratio =
`(6\pi)/(6)`

Ratio = π

When the diameter is 12 inches

C₂ = 12 π

Ratio of circumference to diameter

Ratio =
`(12\pi)/(12)`

Ratio = π

Now, the correct statement is the ratio of the circumference to its diameter remains the same if the diameter is doubled.