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
Derivation of Formula for Area of Cyclic Quadrilateral
For a cyclic quadrilateral with given sides a, b, c, and d, the formula for the area is given by
Where s = (a + b + c + d)/2 known as the semi-perimeter.
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001 Solid steel ball remolded into hollow steel ball
Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
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