Question

A saucer has a radius of $8\mathrm{cm}.$ A plate has a radius of $12\mathrm{cm}.$ How much larger is the circumference of the plate than the circumference of the saucer?

Answer 1

Solve for the required value:

Given: Radius of the saucer, ${\mathrm{r}}_{\mathrm{s}}=8\mathrm{cm}$ and radius of the plate, ${\mathrm{r}}_{\mathrm{p}}=12\mathrm{cm}$.

As the circumference of a circle $=2\mathrm{\pi r}$, where $\mathrm{r}$ is the radius of a circle.

So, the circumference of the saucer, ${\mathrm{C}}_{\mathrm{s}}=2{\mathrm{\pi r}}_{\mathrm{s}}$ and circumference of the plate, ${\mathrm{C}}_{\mathrm{p}}=2{\mathrm{\pi r}}_{\mathrm{p}}$

Now, the difference between the circumference of plate and saucer $={\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{s}}$

$=2{\mathrm{\pi r}}_{\mathrm{p}}-2{\mathrm{\pi r}}_{\mathrm{s}}$

$=2\mathrm{\pi }\left(12\right)-2\mathrm{\pi }\left(8\right)$

$=2\mathrm{\pi }\left(12-8\right)$

$=2\times 3.14\times \left(4\right)$ $\left[\because \mathrm{\pi }=3.14\right]$

$=25.12\mathrm{cm}$

Hence, the circumference of the plate is $25.12\mathrm{cm}$ larger than the circumference of the saucer.