A regular hexagon inscribed in a circle is approximately 0.827 times the area of that same circle. What percentage of the circle
1 answer:
a. The percentage of the circle occupied by the hexagon is 82.7%
b. The percentage of the circle not occupied by the hexagon is 17.3%
Step-by-step explanation:
a regular hexagon inscribed in a circle is approximately 0.827 times the
area of that same circle
1. Assume that area the circle is x
2. Find the ratio of area hexagon to area circle
3. Change The ratio to percentage
4. Subtract area hexagon from area circle to find the area not occupied
by the hexagon and do the same steps 2 and 3 with the area not
occupied and the circle
∵ The regular hexagon inscribed in a circle
∴ Area the circle > area of the hexagon
∵ Area the circle is x
∵ Area the hexagon is 0.827 times the area of the circle
∴ Area hexagon = 0.827(x)
∵ The ratio between area hexagon and area circle =
- Cancel x up with x down
∴ The ratio between area hexagon and area circle = 0.872
- Change the ratio to percentage by multiply it by 100%
∴ The percentage of area hexagon to area circle = 0.827 × 100%
∴ The percentage of area hexagon to area circle = 82.7%
a. The percentage of the circle occupied by the hexagon is 82.7%
∵ Area the circle is x
∵ Area the hexagon is 0.827 x
∴ The area not occupied by the hexagon = x - 0.827 x
∴ The area not occupied by the hexagon = 0.173 x
The ratio between area not occupied by the hexagon and area circle
=
- Cancel x up with x down
∴ The ratio between area not occupied by the hexagon and area
circle = 0.173
- Change the ratio to percentage by multiply it by 100%
∴ The percentage of area not occupied by the hexagon to area
circle = 0.173 × 100%
∴ The percentage of area not occupied by the hexagon to area
circle = 17.3%
b. The percentage of the circle not occupied by the hexagon is 17.3%
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<h2>Hello!</h2>
The answer is:
Ava and Kelly will be 3/4 mile apart after 0.375 hours.
<h2>Why?</h2>To calculate when will Ava and Kelly be 3/4 mile apart, we need to write the equations for both Ava's and Kelly's positions.
Writing the equations we have:
For Ava:
For Kelly:
We need to calculate when Kelly will be 3/4 mile apart becase is running faster than Ava, so, writing the equation we have:
Now, substituting the equation for Ava into the equation for Kelly, we have:
To prove that the result is correct, we just need to substitute the obtained value for time into both equations, so, substutiting we have:
For Ava:
For Kelly:
There is a difference of 0.75 miles or 3/4 mile between Ava and Kelly, so, the obtained value for time is correct.
Therefore, we have that Ava and Kelly will be 3/4 mile apart after 0.375 hours.
Have a nice day!