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Total Area of a Frustum of a Right Circular Cone

In geometry, a frustum is the portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it.The total area of a frustum ... more

Surface area of a right regular pyramid

The surface of a right regular pyramid can be calculated by the area and the perimeter of the base and the slant height

... more

Surface area of a right regular cone

The lateral surface area of a cone including the area of the base, can be calculated by the radius of the circle at the bottom of the cone and the lateral ... more

Lateral surface area of a right circular cone

The lateral surface area of a cone (excluded the area of the base) can be calculated by the radius of the circle at the bottom of the cone and the lateral ... more

Optimum conical horn antenna

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are ... more

Optimum pyramidal horn antenna - H-field

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are ... more

Optimum pyramidal horn antenna - E-field

A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are ... more

Volume of a pyramid (The base is a regular polygon)

A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid ... more

Pyramid frustum (volume)

A pyramid frustum is the portion of a pyramid that lies between two parallel planes cutting it.
The volume of a pyramid frustum is related with the ... more

Volume of a pyramid

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a ... more

Pyramid frustum's volume (n-sided regular polygon bases)

A pyramid frustum is the portion of a pyramid that lies between two parallel planes cutting it. The volume of a pyramid frustum, whose bases are n-sided ... more

Slant Range

In radio electronics, especially radar terminology, slant range is the line-of-sight distance between two points which are not at the same level relative ... more

Volume of any right circular cone

Right circular cone is assumed to be a cone that its base is a circle and right means that the axis passes through the centre of the base at right angles ... more

Volume of cone (by the diameter)

Description

A cone is an n-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or ... more

Volume of a cone - circular

A cone is an n-dimensional geometric shape that tapers smoothly from a base (usually flat and circular) to a point called the apex or vertex. It is the ... more

Height of a regular tetrahedron

The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. A ... more

Volume of a bipyramid (base regular n-sided polygon)

An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal
pyramid and its mirror image base-to-base.
The volume of a ... more

Curved Area of a Frustum of a Right Circulacircular Cone

The curved area of the frustum cone, can be calculated from the radius of the lower base and the radius of the upper base and the height of the cone (the ... more

Volume of a Frustum of a Right Circular Cone

The volume can be calculated from the height of the cone, the radius of the lower base and the radius of the upper base

... more

Relation between the inradius,exradii,circumradius and the distances of the orthocenter from the vertices of a triangle

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

Moment of Inertia - Sphere (solid) - y axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Moment of Inertia - Right Circular Cone - x and y axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Volume of a Square Pyramid

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.

... more

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Inradius of arbitrary triangle

The radius of the inscribed circle of an arbitrary triangle is related to the altitudes of the triangle

... more

Sum of consecutive (pyramidal) squares

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square ... more

Volume of a tetrahedron

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. It has six edges and four ... more

Moment of Inertia - Right Circular Cone - z axis

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

Nose cap Spherically blunted tangent ogive shape ( X-coordinate of the center)

The tangent ogive shape nose-cap is the most familiar in hobby rocketry. The profile of this shape is formed by a segment of a circle such that the rocket ... more

Nose cone (Spherical)

The nose cone section of any vehicle or body meant to travel through a compressible fluid medium (such as a rocket or aircraft, missile or bullet) is ... more

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