Question

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

Answer 1

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

Answer 2

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

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