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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Verified Answer :

JeanaShupp JeanaShupp · Answer 1 · 2019-01-30T14:09:56-05:00

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=\(\pi d\)

Given: The circumference is increased from \(12\pi\ cm\ to\ 18\pi\ cm\)

It implies the increase in the circumference=\(\pi d_2-\pi d_1=18\pi-12\pi\), where \(d_1\) is the previous diameter and \(d_2\)

is the new diameter.

\(\Rightarrow\pi(d_2-d_1)=\pi(18-12)\\\Rightarrow(d_2-d_1)=6\)

Hence, the increase in the diameter= 6 cm

MrRoyal MrRoyal · Answer 2 · 2022-02-08T06:55:06-05:00

The diameter of the circle must increase by 6

The circumference of a circle is calculated as:

\(C = \pi d\)

Given that:

\(C_1 = 12\pi\) --- the initial circumference

\(C_2 = 18\pi\) --- the final circumference

So, we have:

\(\pi d_1 =12\pi\)

\(\pi d_2 =18\pi\)

Where:

\(d_2 = d + d_1\)

So, we have:

\(\pi d_2 = \pi (d + d_1)\)

\(\pi (d + d_1) = 18\pi\)

Subtract \(\pi d_1 =12\pi\) from \(\pi (d + d_1) = 18\pi\)

\(\pi(d + d1 - d1) = 18\pi - 12\pi\)

\(\pi(d) = 6\pi\)

Divide both sides by \(\pi\)

\(d= 6\)

Hence, the diameter must increase by 6