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
 

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
 

SI Unit Prefixes

Prefix Symbol Factor Decimal
Yocto Septillionth y 10-24   0.000000000000000000000001
Zepto Sextillionth z 10-21   0.000000000000000000001
Atto Quintillionth a 10-18   0.000000000000000001
Femto Quadrillionth f  10-15   0.000000000000001
Pico Trillionth p  10-12   0.000000000001
Nano Billionth n  10-9   0.000000001
Micro  Millionth µ  10-6   0.000001
Milli Thousandth m  10-3   0.001
Centi Hundredth c 10-2   0.01
Deci  Tenth d  10-1   0.1
  One   100 1
Deca  Ten da  101 10  
Hecto Hundred h  102 100  
Kilo Thousand k  103 1000  
Mega Million M  106 1000000  
Giga Billion G  109 1000000000  
Tera Trillion T  1012 1000000000000  
Peta Quadrillion P  1015 1000000000000000  
Exa Quintillion E  1018 1000000000000000000  
Zetta Sextillion Z  1021 1000000000000000000000  
Yotta Septillion Y  1024 1000000000000000000000000   
 

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.
 

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
 

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
 

$A = \sqrt{s(s - a)(s - b)(s - c)}$

 

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
 

$d_1 d_2 = ac + bd$

 

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
 

$A = \sqrt{(s - a)(s - b)(s - c)(s - d)}$

 

Where s = (a + b + c + d)/2 known as the semi-perimeter.
 

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.
 

001 A wire of given density and total mass

Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.

  1. What is the density of the wire in kg/m3?
  2. Find the volume of the wire in cubic centimeter.
  3. If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.

 

Pages

Subscribe to MATHalino RSS