Where Can I Get a Traffic Cone?

Look online. Or even at flea markets. But make sure if you put a cone out there, it wo not be considered a crime.

Where Can I Get a Traffic Cone? 1

1. If the TSA of a cone and a hemisphere is 858 and the slant height of a cone is 24, what will be its total height?

Definitions:Let S be the slant height of the right circular cone. Let R be the radius of the sphere. Let A be the radius of the base of the cone. Let H be the segment of the height of the cone that overlaps with the radius of the sphere. Let theta be the angle between the axis of the cone and the line connecting the sphere's center to a point on the cone's base's circumference. We are looking for the total height h of the structure, given S and the surface area P. I will denote X as the part of P contributed by the sphere and Y as the part of P contributed by the cone. Case A:The sphere lies on top of the cone so that exactly a hemisphere is contributing to the surface area.Case B:The sphere lies on top of the cone so that the cone 's sides are tangent to the sphere. This gives a smoother, more "natural" structure. Answer:Case A:By the Pythagorean theorem, h=RsqrtS^2-R^2 where R=fracsqrtpi^2S^28pi P-pi S4pi.Substituting in S=24 and P=858 for the question, we get Rapprox 7.14 and therefore happrox 30.05.Case B:By the Pythagorean theorem, h=RsqrtS^2R^2 where R satisfies XY=P where X=2pi R^21 cos[arctan(fracSR)] and Y=pi RSsin[arctan(fracSR)]. Substituting in S=24 and P=858 for the question, we get Rapprox 6.77 and therefore happrox 31.71.Reasoning:Note that the surface area (sphere) of an entire sphere is 4pi R^2 and the surface area (cone) of a cone (not including its base) is pi AS.Case A:The surface area of this structure will be the surface area of the hemisphere added to the surface area of the cone (not including its base). X=frac12Area(Sphere)=frac12(4pi R^2)=2pi R^2.nAlso, Y=pi AS=pi RS since A=R in this case.So P=2pi R^2pi RS.Applying the quadratic formula, we have R=fracsqrtpi^2S^28pi P-pi S4pi, which is used in the answer. Case B:Note that tan(theta)=fracSR. So we know that theta=arctan(fracSR), which is a function of only R if S is given.Note that sin(theta)=fracAR. So we know that A=Rsin(theta), which is a function of only R if S is given.Note that H is the remnant of the radius R (overlapping with the cone's height) when its non-overlapping part with the cone is removed. By utilizing the Pythagorean theorem, H=R-sqrtR^2-A^2, which is a function of only R if S is given.The surface area of this structure will be the surface area of the part of the sphere above the cone added to the surface area of the cone (not including its base). Note that X will be the sphere's full surface area but subtracting off the surface area of the Spherical Cap covered by the cone (equals 2pi RH). So P=(4pi R^2-2pi RH)pi AS. Substituting in for A, H, and subsequently theta in this equation, we get one equation with one unknown variable R:P=XY where X=2pi R^21 cos[arctan(fracSR)] and Y=pi RSsin[arctan(fracSR)]. The solution for R in this equation is used in the answer.If the TSA of a cone and a hemisphere is 858 and the slant height of a cone is 24, what will be its total height?.

2. If a cone with a height of 16 cm is carved out of a solid sphere with a radius of 10 cm, what will be the radius of the cone?

The height of the cone would extend beyond the center of the sphere by 6cm and be the center of the base of the cone. Let's call this 6 cm segment AB. At right angles to this segment to the spheres circumstances would be the radius of the cone's base. Let's call this radius BC. Then from the center of the sphere to the point where the cone's radius meet would be at point C. A right triangle ABC would form with one side 6 cm and the hypotenuse, AC, would be the radius of the sphere. These measurements would constitute at 3-4-5 right triangle. AB = 6, BC = 8 & AC = 10. The radius of the cone, BC = 8 cm is the answer to the question. Q. E. D. If a cone with a height of 16 cm is carved out of a solid sphere with a radius of 10 cm, what will be the radius of the cone?

Where Can I Get a Traffic Cone? 2

3. Tip of cone $CA=(Atimes I)/(Atimes 0)$ is contained in the interior of $CA$

$Atimes ,.5)/ A times 0$ is open in $CA$ by definition of the quotient topology. Since preimage of $Atimes ,.5)/ A times 0$ under the quotient map from $X sqcup CA$ is itself, this then implies that $Atimes ,.5)/ A times 0$ is open in the glued space. This means the tip of the cone is in the interior

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