Question

You resize a picture so that the radius of the midday Sun appears four times larger. How much larger does the circumference of the Sun appear? Explain

Answer 1

The radius and circumference of a circle are directly related, which means larger the radius of a circle larger will be its circumference and vice-versa.

Let’s assume that radius of midday Sun before resizing the picture was $r$ and after resizing it becomes $R$.

We know that,

Circumference (C) = $2\mathrm{\pi r}$

After resizing the picture radius of the Sun has increased four times, i.e.,

$$\begin{gathered} R=4\times r \\ R=4r \end{gathered}$$

Now, new circumference (C*) will be given by

$C*=2\pi R$

$C*=2\pi \times 4r$

$C*=4\times 2\pi r$

$C*=4C$

Hence When radius of the midday Sun appear four times larger, circumference of the Sun will also appear four times larger.