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.

please helppp ​

Answer 1

`\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 \: √(80) \: = \: r`

`\large\purple\implies \rm \large \:4 √(5) \: = \: r`

Hence , the radius of circle is 4√5.

Answer 2

`r=4√(5)\:\: \sf m`

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 (80 \pi)/(\pi) = (\pi r^2)/(\pi)`

`\implies 80=r^2`

`\implies √(r^2)=√(80)`

`\implies r=√(80)`

`\implies r=√(16 \cdot 5)`

`\implies r=√(16)√(5)`

`\implies r=√(4^2)√(5)`

`\implies r=4√(5)`