Question

If the area of a circle is 16 square meters, what is its radius in meters?

A 4√ππ

B 8/π

D 12π

C 16/π

E 16 π

Answer 1

`r = \bf (4 \sqrt \pi)/(\pi)`

Explanation:

In order to solve this problem, we have to use the formula for the area of a circle:

`\boxed{A = \pi r^2}`

where:

A ⇒ area of the circle = 16 m²

r ⇒ radius of the circle

Since we already know the area of the circle, we can substitute the given value into the formula above and then solve for r to get the radius of the circle:

`16 = \pi * r^2`

⇒
`r^2 = (16)/( \pi)` [Dividing both sides of the equation by π]

⇒
`r = \sqrt{(16)/(\pi)}` [Taking the square root of both sides of the equation]

⇒
`r = \frac{\sqrt {16}}{\sqrt \pi}` [Distributing the square root]

⇒
`r = \bf (4)/(\sqrt \pi)`

It is usually encouraged to remove the square root from the denominator of a fraction. To do this we can multiply both the numerator and the denominator by the square root:

`r = (4 * √(\pi))/(\sqrt \pi * \sqrt \pi)`

⇒
`r = \bf (4 \sqrt \pi)/(\pi)`

Therefore, the correct answer is A.

Answer 2

`\displaystyle{r=(4√(\pi))/(\pi)}`

Explanation:

The area of a circle is
`\displaystyle{\pi r^2}`. Since the area equals 16 m² then set the equation:

`\displaystyle{\pi r^2 = 16}`

Solve for the radius (r) by dividing both sides by
`\pi`:

`\displaystyle{(\pi r^2)/(\pi) = (16)/(\pi)}\\\\\displaystyle{r^2 = (16)/(\pi)}`

Square root both sides, only positive values exist so no plus-minus:

`\displaystyle{√(r^2) = \sqrt{(16)/(\pi)}}\\\\\displaystyle{r = (4)/(√(\pi))`

Conjugate by multiplying both denominator and numerator by
`√(\pi)`:

`\displaystyle{r=(4\cdot √(\pi))/(√(\pi)\cdot√(\pi))}\\\\\displaystyle{r=(4√(\pi))/(\pi)}`

Hence, the answer is A.