Answer:
Explanation:
If the cone in question 22 is made of paper and the paper is flattened out into the sector of a circle, the angle of the sector can be calculated as follows:
A cone is created from a paper circle with a 90° sector cut from it.
The paper along the remaining circumference of the circle is the base of the cone.
The angle (in radians) of a circular sector is a ratio of the arc length and the sector’s radius.
The arc length is a circumference of your cone’s base. l = 2 π r .
The radius is a slant height of the cone, i.e. the distance from the apex to the base edge: R = h² + r² .
Therefore, we can calculate the angle of the sector as follows:
Let r be the radius of the base of the cone.
Let h be the height of the cone.
We know that 90° was cut from a circle to create this cone.
Therefore, we can say that 90° = π/2 radians.
We also know that l = 2 π r and R = h² + r².
Since l is equal to the circumference of a circle with radius r, we can say that l = 2 π r = 2 π (h² + r²) / (2h).
Simplifying this equation gives us l = πr² / h + h.
We can now use this equation to solve for r.
If we substitute r = 6 into this equation, we get l = 12π / 5 + 5.
Therefore, l ≈ 7.39.
Now that we know l and r, we can use R = h² + r² to solve for h.
If we substitute r = 6 into this equation and solve for h, we get h ≈ 7.75.
Finally, we can use R = h² + r² to solve for R.
If we substitute r = 6 and h ≈ 7.75 into this equation, we get R ≈ 12.19.
Therefore, if the cone in question 22 is made of paper and flattened out into a sector of a circle, then the angle of that sector is approximately 1.28 radians.
I hope this helps!