Question

two circles have their radii in the ratio 1 : 2 if the radius of a circle is doubled and that of the Other circle is Hafte then what would be the ratio of circumference and areas of the new circles​

Answer 1

Answer: The ratio of the circumference of circles is $\bold{2:1}$ and the ratio of the areas is $\bold{4:1}$.

Given: Ratio of radius of two circle is 1 : 2.

To Find: Ratio of circumference and areas of the new circles.

Step-by-step explanation:

Step 1: Let the radius of first circle is x and second circle is 2x.

Now, new radius of the first circle is 2x and second circle is x.

The circumference of a circle is its edge or the measurement of its entire arc.

Then, circumference of the first circle $=2\pi r_1=2\pi (2x)=4x\pi$

Circumference of the second circle$=2\pi r_2=2\pi (x)=2x\pi$

The ratio of circumference $=4x\pi:2x\pi=2:1$

Hence, the ratio of the circumference of circles is $\bold{2:1}$.

Step 2: The radius squared is multiplied to find the area of a circle. When the radius 'r' is known, the area of a circle (A) is equal to $\pi r^2$. $\pi$ is approximately 3.14 or 22/7.

Area of the first new circle $=2\pi {r_1}^2=2\pi (2x)^2=8x^2 \pi$

Area of the second new circle $=2\pi {r_2}^2=2\pi (x)^2=2x^2 \pi$

The ratio of areas $= 8x^2 \pi:2x^2\pi=4:1$

Hence, the ratio of the areas is $\bold{4:1}$.

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