Volume=43πr3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi r^{3}} π=3. 14{\displaystyle \pi =3. 14} r=radius{\displaystyle r={\text{radius}}}
Suppose you are told that a sphere exists with a radius of 10 cm. Find the volume as follows: Volume=43πr3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi r^{3}} Volume=43∗(3. 14)∗103{\displaystyle {\text{Volume}}={\frac {4}{3}}*(3. 14)10^{3}} Volume=4. 18667∗1000{\displaystyle {\text{Volume}}=4. 186671000} Volume=4186. 67cm3{\displaystyle {\text{Volume}}=4186. 67{\text{cm}}^{3}}
Volume=43π(d2)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {d}{2}})^{3}} As an example of this calculation, find the volume of a sphere whose diameter is 10 cm. Volume=43π(d2)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {d}{2}})^{3}} Volume=43π(102)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {10}{2}})^{3}} Volume=43∗(3. 14)∗(53){\displaystyle {\text{Volume}}={\frac {4}{3}}(3. 14)(5^{3})} Volume=4. 18667∗125{\displaystyle {\text{Volume}}=4. 18667*125} Volume=523. 3cm3{\displaystyle {\text{Volume}}=523. 3{\text{cm}}^{3}}
Volume=43πr3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi r^{3}} Volume=43π∗(C2π)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi *({\frac {C}{2\pi }})^{3}} Volume=43π∗(C38π3){\displaystyle {\text{Volume}}={\frac {4}{3}}\pi *({\frac {C^{3}}{8\pi ^{3}}})} Volume=C36π2{\displaystyle {\text{Volume}}={\frac {C^{3}}{6\pi ^{2}}}}
Volume=C36π2{\displaystyle {\text{Volume}}={\frac {C^{3}}{6\pi ^{2}}}} Volume=3236∗3. 142{\displaystyle {\text{Volume}}={\frac {32^{3}}{6*3. 14^{2}}}} Volume=32,76859. 158{\displaystyle {\text{Volume}}={\frac {32,768}{59. 158}}} Volume=553. 9cm3{\displaystyle {\text{Volume}}=553. 9{\text{cm}}^{3}}
Pour enough water into the beaker to cover the sphere. Make note of the measurement. Place the sphere into the water. Notice that the water level rises. Make note of the new measurement. Subtract the first measurement from the second. The result is the volume of the sphere. For example, suppose your water level rises from 100 ml to 625 ml when you submerge the sphere. The volume is therefore 525 ml. Note that 1 ml=1 cm3.
You can find densities of many solid materials by looking up density tables online, in textbooks or in other industry catalogs. For example, here are the recorded densities of some solid materials:[7] X Research source Aluminum = 2700 kg/m3 Butter = 870 kg/m3 Lead = 11,350 kg/m3 Pressed wood = 190 kg/m3
All of the examples in the previous section resulted in volumes measured in cubic centimeters. However, the cited density table provides densities based on cubic meters. Because there are 100 centimeters in a meter, there are 106 cubic centimeters in a cubic meter. Divide the given densities by 106 to represent the density in units of kg/cm3. (You can do this most easily by just moving the decimal point 6 spaces to the left. ) For the four sample materials, the converted densities are as follows: Aluminum = 2700 kg/m3 = 0. 0027 kg/cm3 Butter = 870 kg/m3 = 0. 00087 kg/cm3 Lead = 11,350 kg/m3 = 0. 01135 kg/cm3 Pressed wood = 190 kg/m3 = 0. 00019 kg/cm3
Using the four sample materials, aluminum, butter, lead and pressed wood, find the mass of a sphere that has a volume of 500 cm3. Aluminum:500 cm3∗0. 0027kgcm3=1. 35 kg{\displaystyle {\text{Aluminum}}:500{\text{ cm}}^{3}*0. 0027{\frac {\text{kg}}{{\text{cm}}^{3}}}=1. 35{\text{ kg}}} Butter:500 cm3∗0. 00087kgcm3=0. 435 kg{\displaystyle {\text{Butter}}:500{\text{ cm}}^{3}*0. 00087{\frac {\text{kg}}{{\text{cm}}^{3}}}=0. 435{\text{ kg}}} Lead:500 cm3∗0. 01135kgcm3=5. 675 kg{\displaystyle {\text{Lead}}:500{\text{ cm}}^{3}*0. 01135{\frac {\text{kg}}{{\text{cm}}^{3}}}=5. 675{\text{ kg}}} Pressed wood:500 cm3∗0. 00019kgcm3=0. 095 kg{\displaystyle {\text{Pressed wood}}:500{\text{ cm}}^{3}*0. 00019{\frac {\text{kg}}{{\text{cm}}^{3}}}=0. 095{\text{ kg}}}
A large sphere made of solid brass has a diameter of 1. 2 m. Find the mass of the sphere.
Volume=43π(d2)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {d}{2}})^{3}} You should also notice that the sphere is made of brass. You will need to look up the density of brass from a density table online. From the website, EngineeringToolbox. com, you can find that the density of brass is 8480 kg/m3. Because the diameter of the sphere was given in meters, its volume will be calculated in cubic meters, so you do not need to convert the density.
Volume=43π(d2)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {d}{2}})^{3}} Volume=43π(1. 22)3{\displaystyle {\text{Volume}}={\frac {4}{3}}\pi ({\frac {1. 2}{2}})^{3}} Volume=4. 18667∗0. 63{\displaystyle {\text{Volume}}=4. 186670. 6^{3}} Volume=4. 18667∗0. 216{\displaystyle {\text{Volume}}=4. 186670. 216} Volume=0. 90432 m3{\displaystyle {\text{Volume}}=0. 90432{\text{ m}}^{3}}
Mass=Density∗Volume{\displaystyle {\text{Mass}}={\text{Density}}*{\text{Volume}}} Mass=8480 kg m3∗0. 90432 m3{\displaystyle {\text{Mass}}=8480{\frac {\text{ kg}}{{\text{ m}}^{3}}}*0. 90432{\text{ m}}^{3}} Mass=7668. 6 kg{\displaystyle {\text{Mass}}=7668. 6{\text{ kg}}}
