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Cone distance of bevel gear is the general term for the distance along with an element of the pitch Cone from the apex to any given position in the teeth. Outer Cone distance in bevel gears is the distance from the apex of the pitch Cone to the outer ends of the teeth.

A 0 = \sqrt{{(\frac{D p}{2})}^{2} + {(\frac{D g}{2})}^{2}}

Friction Torque on Cone Clutch from Constant Wear Theory given Semi-Cone Angle

Friction Torque on Cone Clutch from Constant Wear Theory given Semi-Cone Angle formula is defined as the measure of rotational force that opposes motion in a Cone clutch system, influenced by the semi-Cone angle, and is a critical parameter in the design and optimization of Cone clutches in various mechanical systems.

M T = π \cdot μ \cdot p a \cdot d i \cdot \frac{({d o}^{2}) - ({d i}^{2})}{8 \cdot \sin (α)}

Mass of Cone

The Mass of Cone formula is defined as the 1/3 times of π multiplied to the product of density of Cone, height of Cone and square of the radius of the Cone.

M co = \frac{1}{3} \cdot π \cdot ρ \cdot H c \cdot {R c}^{2}

Volume of Cone

Volume of Cone formula is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

V = \frac{π \cdot {r Base}^{2} \cdot h}{3}

Base Area of Cone

Base Area of Cone formula is defined as the total quantity of plane enclosed on the base circular surface of the Cone.

A Base = π \cdot {r Base}^{2}

Slant Height of Cone

Slant Height of Cone formula is defined as the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base of the Cone.

h Slant = \sqrt{h^{2} + {r Base}^{2}}

Volume of Truncated Cone

Volume of Truncated Cone formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.

V = \frac{π}{3} \cdot h \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2})

Volume of Frustum of Cone

Volume of Frustum of Cone formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone.

V = \frac{1}{3} \cdot π \cdot h \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))

Nose Radius of Sphere Cone

The Nose Radius of Sphere Cone formula is defined as a measure of the radius of a sphere Cone in hypersonic inviscid flow, which is a critical parameter in aerodynamics and aerospace engineering, used to study the behavior of fluids at high speeds and low densities.

r = \frac{𝛿}{0.143 \cdot \exp (\frac{3.24}{M^{2}})}

Total Surface Area of Cone

Total Surface Area of Cone formula is defined as the total quantity of plane enclosed on the entire surface of the Cone.

TSA = π \cdot r Base \cdot (r Base + h Slant)

Base Circumference of Cone

Base Circumference of Cone formula is defined as the total length of the boundary of the base circular surface of the Cone.

C Base = 2 \cdot π \cdot r Base

Top Area of Truncated Cone

The Top Area of Truncated Cone formula is defined as the total amount of two-dimensional space occupied by the top face of the Truncated Cone.

A Top = π \cdot {r Top}^{2}

Base Area of Truncated Cone

The Base Area of Truncated Cone formula is defined as the total amount of two-dimensional space occupied by the base face of the Truncated Cone.

A Base = π \cdot {r Base}^{2}

Height of Cone given Volume

Height of Cone given Volume formula is defined as the distance between the apex of the Cone to the center of the circular base, and calculated using the volume of the Cone.

h = \frac{3 \cdot V}{π \cdot {r Base}^{2}}

Top Area of Frustum of Cone

Top Area of Frustum of Cone formula is defined as the total amount of two-dimensional space occupied by the top face of the Frustum of Cone.

A Top = π \cdot {r Top}^{2}

Base Area of Frustum of Cone

Base Area of Frustum of Cone formula is defined as the total amount of two-dimensional space occupied by the base face of the Frustum of Cone.

A Base = π \cdot {r Base}^{2}

Lateral Surface Area of Cone

Lateral Surface Area of Cone formula is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone.

LSA = π \cdot r Base \cdot h Slant

Back Cone Radius of Bevel Gear

Back Cone Radius of Bevel Gear is defined as the length of the back Cone element. The back Cone of a bevel gear is an imaginary Cone tangent to the outer ends of the teeth, with its elements perpendicular to those of the pitch Cone.

r b = \frac{m \cdot z'}{2}

Volume of Cone given Base Area

Volume of Cone given Base Area formula is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone, and calculated using the base area of the Cone.

V = \frac{A Base \cdot h}{3}

Slant Height of Truncated Cone

The Slant Height of Truncated Cone formula is defined as the length of the straight line connecting any point on the base to the truncated top circular face of the Truncated Cone.

h Slant = \sqrt{{(r Base - r Top)}^{2} + h^{2}}

Base Area of Cone given Volume

The Base Area of Cone given Volume formula is defined as the total quantity of plane enclosed on the base circular surface of the Cone, and calculated using the volume of the Cone.

A Base = \frac{3 \cdot V}{h}

Slant Height of Frustum of Cone

Slant Height of Frustum of Cone formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone.

h Slant = \sqrt{h^{2} + {(r Top - r Base)}^{2}}

Base Radius of Cone given Volume

Base Radius of Cone given Volume formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone, and calculated using the volume of the Cone.

r Base = \sqrt{\frac{3 \cdot V}{π \cdot h}}

Slant Height of Cone given Volume

Slant Height of Cone given Volume formula is defined as the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base of the Cone, and calculated using the volume of the Cone.

h Slant = \sqrt{{(\frac{3 \cdot V}{π \cdot {r Base}^{2}})}^{2} + {r Base}^{2}}

Height of Cone given Slant Height

Height of Cone given Slant Height formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the slant height of the Cone.

h = \sqrt{{h Slant}^{2} - {r Base}^{2}}

Field Density in Sand Cone Method

The Field Density in Sand Cone Method formula is defined as the ratio of weight of soil to volume of soil and it is used for determination of compaction in soil.

ρ fd = (\frac{W t}{V})

Radius for Sphere-Cone Body Shape

Radius for Sphere-Cone Body Shape formula is defined as a mathematical representation of the radius of a sphere-Cone body shape, which is a critical parameter in hypersonic flight paths, particularly in velocity of altitude map analysis, where it plays a vital role in determining the aerodynamic characteristics of a vehicle.

r = \frac{R curvature}{1.143 \cdot \exp (\frac{0.54}{{(M r - 1)}^{1.2}})}

Volume of Cone given Slant Height

The Volume of Cone given Slant Height formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the slant height of the Cone.

V = \frac{π \cdot {r Base}^{2} \cdot \sqrt{{h Slant}^{2} - {r Base}^{2}}}{3}

Weight of Soil in Sand Cone Method

The Weight of Soil in Sand Cone Method formula is defined as the weight of the soil removed from a test hole in sand Cone test, thus allowing for the calculation of the soil's density.

W t = (ρ fd \cdot V)

Base Radius of Cone given Base Area

Base Radius of Cone given Base Area formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone, and calculated using the base area of the Cone.

r Base = \sqrt{\frac{A Base}{π}}

Total Surface Area of Truncated Cone

The Total Surface Area of Truncated Cone formula is defined as the quantity of plane enclosed by the entire surface of the Truncated Cone.

TSA = π \cdot ({r Base}^{2} + {r Top}^{2} + (\sqrt{{(r Top - r Base)}^{2} + h^{2}} \cdot (r Base + r Top)))

Base Area of Cone given Slant Height

The Base Area of Cone given Slant Height formula is defined as the total quantity of plane enclosed on the base circular surface of the Cone, and calculated using the slant height of the Cone.

A Base = π \cdot ({h Slant}^{2} - h^{2})

Percent Moisture in Sand Cone Method

The Percent Moisture in Sand Cone Method formula is defined as a measure of the amount of water present in a soil sample, expressed as a percentage of the dry weight of the soil. The Sand Cone Test is primarily used to determine the in-place density of soil, which is crucial for compaction control in geotechnical engineering.

M sc = \frac{100 \cdot (W m - W d)}{W d}

Height of First Cone of Double Point

Height of First Cone of Double Point formula is defined as the distance between the center of circular face and apex of the first Cone attached to the cylindrical portion in the Double Point.

h First Cone = l - h Cylinder - h Second Cone

Height of Second Cone of Double Point

Height of Second Cone of Double Point formula is defined as the distance between the center of circular face and apex of the second Cone attached to the cylindrical portion in the Double Point.

h Second Cone = l - h Cylinder - h First Cone

Curved Surface Area of Truncated Cone

The Curved Surface Area of Truncated Cone formula is defined as the quantity of plane enclosed on curved surfaces (that is, top and bottom faces are excluded) of the Truncated Cone.

CSA = π \cdot (r Base + r Top) \cdot \sqrt{{(r Base - r Top)}^{2} + h^{2}}

Height of Truncated Cone given Volume

The Height of Truncated Cone given Volume formula is defined as the vertical distance from the base circular surface to the top most point of the Truncated Cone, and calculated using the volume of Truncated Cone.

h = \frac{3 \cdot V}{π \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2})}

Total Surface Area of Frustum of Cone

The Total Surface Area of Frustum of Cone formula is defined as the total quantity of plane enclosed on the entire surface of the Frustum of Cone.

TSA = π \cdot (((r Top + r Base) \cdot \sqrt{{(r Top - r Base)}^{2} + h^{2}}) + {r Top}^{2} + {r Base}^{2})

Height of Frustum of Cone given Volume

The Height of Frustum of Cone given Volume formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the volume, top radius, and base radius of the Frustum of Cone.

h = \frac{3 \cdot V}{π \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))}

Base Radius of Cone given Slant Height

The Base Radius of Cone given Slant Height formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone, and calculated using the slant height of the Cone.

r Base = \sqrt{{h Slant}^{2} - h^{2}}

Curved Surface Area of Frustum of Cone

Curved Surface Area of Frustum of Cone formula is defined as the quantity of plane enclosed by curved surfaces (that is, top and bottom faces are excluded) of the Frustum of Cone.

CSA = π \cdot (r Top + r Base) \cdot \sqrt{{(r Top - r Base)}^{2} + h^{2}}

Volume of Cone given Base Circumference

Volume of Cone given Base Circumference formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the base circumference of the Cone.

V = \frac{{C Base}^{2} \cdot h}{12 \cdot π}

Base Circumference of Cone given Volume

Base Circumference of Cone given Volume formula is defined as the total length of the boundary of the base circular surface of the Cone, and calculated using the volume of the Cone.

C Base = 2 \cdot π \cdot \sqrt{\frac{3 \cdot V}{π \cdot h}}

Dry Density of Soil in Sand Cone Method

The Dry Density of Soil in Sand Cone Method formula is defined as the dry density of soil calculated using the relationship used in the procedure of sand Cone method. The sand Cone method is a commonly used in-situ test to determine the field density and dry density of soil. It involves using a calibrated sand Cone apparatus, which includes a jar filled with dry sand, a Cone with a valve, and a base plate.

ρ d = (\frac{γ t}{1 + (\frac{M}{100})})

Height of Cone given Total Surface Area

The Height of Cone given Total Surface Area formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the total surface area of the Cone.

h = \sqrt{{(\frac{TSA}{π \cdot r Base} - r Base)}^{2} - {r Base}^{2}}

Total Surface Area of Cone given Height

The Total Surface Area of Cone given Height formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the height of the Cone.

TSA = π \cdot {r Base}^{2} + π \cdot r Base \cdot \sqrt{h^{2} + {r Base}^{2}}

Total Surface Area of Cone given Volume

The Total Surface Area of Cone given Volume formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the volume of the Cone.

TSA = \frac{3 \cdot V}{h} + π \cdot r Base \cdot \sqrt{{(\frac{3 \cdot V}{π \cdot {r Base}^{2}})}^{2} + {r Base}^{2}}

Volume of Cone given Total Surface Area

The Volume of Cone given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the total surface area of the Cone.

V = \frac{π \cdot {r Base}^{2} \cdot \sqrt{{(\frac{TSA}{π \cdot r Base} - r Base)}^{2} - {r Base}^{2}}}{3}

Volume of Frustum of Cone given Top Area

The Volume of Frustum of Cone given Top Area formula is defined as the quantity of three-dimensional space enclosed by the entire surface of the Frustum of Cone, calculated using the top area, base radius, and height of the Frustum of the Cone.

V = \frac{1}{3} \cdot π \cdot h \cdot (\frac{A Top}{π} + {r Base}^{2} + (\sqrt{\frac{A Top}{π}} \cdot r Base))

Volume of Frustum of Cone given Base Area

The Volume of Frustum of Cone given Base Area formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the base area, top radius and height of the Frustum of Cone.

V = \frac{1}{3} \cdot π \cdot h \cdot ({r Top}^{2} + \frac{A Base}{π} + (r Top \cdot \sqrt{\frac{A Base}{π}}))

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