'

Search results

Found 1073 matches
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

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

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 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

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

Slant height of a right regular pyramid

Slant height is the height of any slant triangle of the regular pyramid, or the distance from the apex, down the side, to a point on the base ... 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

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

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

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

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

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

Surface area 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

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
Vickers hardness number

The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure ... more

Volume of a prism

A prism is a polyhedron with an n-sided polygonal base, a translated copy (not in the same plane as the first), and n other faces (necessarily all ... more

Triangular Prism Volume

A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
... more

Sum of consecutive (triangular) cubes (Nicomachus's theorem)

In number theory, the sum of the first n cubes is the square of the nth triangular number. The sequence of squared triangular numbers is

0, 1, 9, ... 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

Area of a trapezoid

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

Knoop hardness test

The Knoop hardness test /kəˈnuːp/ is a microhardness test – a test for mechanical hardness used particularly for very brittle materials or thin sheets, ... more

Total volume of the two spherical caps of two intersecting spheres

A spherical cap or spherical dome is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of ... more

Area of a right prism (surface area)

Prism is a polyhedron with an n-sided polygonal base, a translated copy (not in the same plane as the first), and “n” other faces (necessarily ... more

Volume of Spherical segment

Spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. The volume can be calculated by the radius of the spherical ... more

Area Moment of Inertia - Filled Right Triangle

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... more

Gain of pyramidal 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

Center of mass of a uniform trapezoid

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

Triangle area

Triangle is a polygon with three edges and three vertices. The area of a triangle with base length b and height length h is given by multiplying base ... 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

...can't find what you're looking for?

Create a new formula