In order to increase the circumference of a circle from 12π cm to 18π cm, by how much must the diameter increase?

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JeanaShupp JeanaShupp · Answer 1 · 2019-01-30T20:09:56+01:00

Answer: The increase in the diameter is 6 cm.

Step-by-step explanation:

The circumference of a circle with diameter 'd' is given by :

Circumference=[tex]\pi d[/tex]

Given: The circumference is increased from [tex]12\pi\ cm\ to\ 18\pi\ cm[/tex]

It implies the increase in the circumference=[tex]\pi d_2-\pi d_1=18\pi-12\pi[/tex], where [tex]d_1[/tex] is the previous diameter and [tex]d_2[/tex]

is the new diameter.

[tex]\Rightarrow\pi(d_2-d_1)=\pi(18-12)\\\Rightarrow(d_2-d_1)=6[/tex]

Hence, the increase in the diameter= 6 cm

MrRoyal MrRoyal · Answer 2 · 2022-02-08T12:55:06+01:00

The diameter of the circle must increase by 6

The circumference of a circle is calculated as:

[tex]C = \pi d[/tex]

Given that:

[tex]C_1 = 12\pi[/tex] --- the initial circumference

[tex]C_2 = 18\pi[/tex] --- the final circumference

So, we have:

[tex]\pi d_1 =12\pi[/tex]

[tex]\pi d_2 =18\pi[/tex]

Where:

[tex]d_2 = d + d_1[/tex]

So, we have:

[tex]\pi d_2 = \pi (d + d_1)[/tex]

[tex]\pi (d + d_1) = 18\pi[/tex]

Subtract [tex]\pi d_1 =12\pi[/tex] from [tex]\pi (d + d_1) = 18\pi[/tex]

[tex]\pi(d + d1 - d1) = 18\pi - 12\pi[/tex]

[tex]\pi(d) = 6\pi[/tex]

Divide both sides by [tex]\pi[/tex]

[tex]d= 6[/tex]

Hence, the diameter must increase by 6