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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

Area moments of inertia for a filled triangular area with respect to an axis through the centroid

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

Liquid in a vertical tube (The height to which the column is lifted )

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon ... 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

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
Marconi's Law

Marconi’s law is the relation between height of antennas and maximum signaling distance of radio transmissions. Guglielmo Marconi enunciated at one ... more

Height of a trapezoid in relation with the sides

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

Capillary Action - height of the meniscus

Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, and ... more

Blade root bending moment load due to yaw

The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more

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