What is the diameter of a circle whose area is #16##pi#?

Question

Maverick Smith · Accepted Answer

#8#

Recall the formula for the area of a circle:

#A=pir^2#, with radius #r#

We see that our radius is #sqrt16#, or #4#.

Recall that the diameter is twice the length of the radius, so we can multiply this by #2# to get a diameter of #8#.

Hope this helps!

Ella Armstrong · Answer

#8#

Use the formula for the area of a circle:

#A=pir^2#

Here, the area is #16pi#:

#16pi=pir^2#

Divide both sides by #pi#:

#16=r^2#

Take the square root of both sides:

#sqrt16=sqrt(r^2)#

#4=r#

Since the radius of the circle is #4#, the diameter is twice that:

#d=4xx2=8#

Maverick Smith · Answer

undefined To find the diameter of a circle given its area, we can use the formula for the area of a circle, which is $ \pi \times \text{radius}^2 $. Given that the area of the circle is $ 16\pi $, we can set up the equation:

$$ \pi \times \text{radius}^2 = 16\pi $$

Solving for the radius, we get:

$$ \text{radius}^2 = \frac{{16\pi}}{\pi} = 16 $$

Taking the square root of both sides to find the radius:

$$ \text{radius} = \sqrt{16} = 4 $$

Finally, the diameter of the circle is twice the radius, so:

$$ \text{diameter} = 2 \times \text{radius} = 2 \times 4 = 8 $$

Therefore, the diameter of the circle is $ 8 $ units.

James Atkins · Answer

undefined To find the diameter of a circle whose area is $16\pi$, you use the formula for the area of a circle: $A = \pi r^2$, where $A$ is the area and $r$ is the radius of the circle. Since the area is given as $16\pi$, you set up the equation:

$$16\pi = \pi r^2$$

Solve for $r$:

$$r^2 = \frac{16\pi}{\pi}$$

$$r^2 = 16$$

$$r = 4$$

The radius of the circle is $4$. The diameter of a circle is twice the radius, so:

$$d = 2r$$

$$d = 2(4)$$

$$d = 8$$

Therefore, the diameter of the circle whose area is $16\pi$ is $8$.