005 Weight of ivory billiard balls
Example 005
A cubic foot of ivory weighs 114 lb. Find the weight of 1000 ivory billiard balls 2½ inch in diameter.
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004 Hemispherical dome covered with gold
Example 004
The surface of a hemispherical dome whose diameter is 10 m is to be covered with gold leaf which costs \$0.25 per square centimeter. What must be paid for the gold leaf?
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003 Weight of an iron shell
Example 003
An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.
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002 Weight of snow ball
Problem 002
Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m3
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SI Derived Units
| Derived quantity | Name | Symbol | Other symbol | Base units |
| plane angle | radian | rad | - | m·m-1 = 1 |
| solid angle |
steradian | sr | - | m2·m-2=1 |
| frequency | hertz | Hz | - | s-1 |
| force | newton | N | - | m·kg·s-2 |
| pressure, stress |
pascal | Pa | N/m2 | m-1·kg·s-2 |
| energy, work, quantity of heat |
joule | J | Nm | m2·kg·s-2 |
| power, radiant flux |
watt | W | J/s | m2·kg·s-3 |
| electric charge, quantity of electricity |
coulomb | C | - | s·A |
| electric potential, difference, electromotive force |
volt | V | W/A | m2·kg·s-3·A-1 |
| capacitance | farad | F | C/V | m-2·kg-1·s4·A2 |
| electric conductance |
siemens | S | A/V | m-2·kg-1·s3·A2 |
| electric resistance | ohm | W | V/A | m2·kg·s-3·A-2 |
| magnetic flux | weber | Wb | Vs | m2·kg·s-2·A-1 |
| magnetic flux density | tesla | T | Wb/m2 | kg·s-2·A-1 |
| inductance | henry | H | Wb/A | m2·kg·s-2·A-2 |
| Celsius temperature | degree Celsius | °C | - | K |
| luminous flux | lumen | lm | cd·sr | m2·m-2·cd = cd |
| illuminance | lux | lx | lm/m2 | m2·m-4·cd = m-2·cd |
| activity (of a radionuclide) | becquerel | Bq | - | s-1 |
| absorbed dose, specific energy (imparted), kerma | gray | Gy | J/kg | m2·s-2 |
| dose equivalent | sievert | Sv | J/kg | m2·s-2 |
| catalytic activity | katal | kat | - | s-1mol |
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SI Unit Prefixes
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SI Base Units
The International System of Units (SI) define the following base units
Meter (m)
The length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.
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The US Customary System of Measures
The following are the English System of measurement
Length
12 inches = 1 foot
3 feet = 1 yard
220 yards = 1 furlong
8 furlongs = 1 mile
5 280 feet = 1 mile
1 760 yards = 1 mile
Area
144 square inches = 1 square foot
9 square feet = 1 square yard
4 840 square yards = 1 acre
640 acres = 1 square mile
1 square mile = 1 section
36 sections = 1 township
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Derivation of Heron's / Hero's Formula for Area of Triangle
For a triangle of given three sides, say a, b, and c, the formula for the area is given by
where s is the semi perimeter equal to P/2 = (a + b + c)/2.
Derivation / Proof of Ptolemy's Theorem for Cyclic Quadrilateral
Ptolemy's theorem for cyclic quadrilateral states that the product of the diagonals is equal to the sum of the products of opposite sides. From the figure below, Ptolemy's theorem can be written as

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