Question

If the ratio of a circle's sector to its total area is 7/8, what is the measure of its sector's arc?

Answer 1

Check the picture below. So the sector looks more or less like that one.

we know a full circle has an arc of 2π, so how much is 7/8 of 2π? well, is simply its product.

`\bf ~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\pi \cdot \cfrac{7}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{7\pi }{4}`