Question

The area of a circle, in terms of π, is 80π m2. Find the value of the radius. Give your answer as a simplified surd.

Answer 1

Answer:

$r=4\sqrt{5}\:\: \sf m$

Step-by-step explanation:

$\textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

Given:

• Area = 80π m²

Substitute the given value into the formula and solve for r:

$\implies 80 \pi = \pi r^2$

$\implies \dfrac{80 \pi}{\pi} = \dfrac{\pi r^2}{\pi}$

$\implies 80=r^2$

$\implies \sqrt{r^2}=\sqrt{80}$

$\implies r=\sqrt{80}$

$\implies r=\sqrt{16 \cdot 5}$

$\implies r=\sqrt{16}\sqrt{5}$

$\implies r=\sqrt{4^2}\sqrt{5}$

$\implies r=4\sqrt{5}$

Answer 2

$\large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {\red{Area \: of \: circle \: = \: πr²}}}}}\end{gathered}$

• Where , r denotes radius of circle.

Substituting , the given values into the formula and solving for r.

$\large\purple\implies \rm \large \:Area \: of \: circle \: = \: πr²$

$\large\purple\implies \rm \large \:80\pi \: = \: \pi {r}^{2}$

$\large\purple\implies \rm \large \:80 \cancel\pi \: = \: \cancel\pi {r}^{2}$

$\large\purple\implies \rm \large \:80 \: = \: {r}^{2}$

$\large\purple\implies \rm \large \: \sqrt{80} \: = \: r$

$\large\purple\implies \rm \large \:4 \sqrt{5} \: = \: r$

Hence , the radius of circle is 4√5.