Question

a hollow metal sphere has an internal radius of 20cm and an external radius of 30cm. given that the density of the metal is 7.8g/cm^3, find the mass of the sphere, expressing your answer in kg.

Answer 1

Find the volume of a solid sphere of radius 30 cm. Subtract the volume of a solid sphere of radius 20 cm. The remaining volume is the volume of your hollow metal sphere. Multiply the volume by the density to get the mass of the metal.

Answer 2

Be careful not to drop it on your toe!

Answer 3

Also, don't forget to watch the units carefully, as the density is expressed in grams/cm^3, but the answer is requested in kg

Answer 4

we know that the volume of the shell is ====> V=(4/3)(pi)r^3...
so Volume of the shell = Volume of 30cm sphere - Vol of 20cm sphere
Volume(shell)=(4/3)(pi)[30^3-20^3]
Volume(shell)=(4/3)(3.14)(27000-8000)
Volume(shell)=(4/3)(3.14)(19000)
Volume(shell)=79546 cm^3
Weight = 7.8(79546)=148200 grams = 148 kgs @insa

Answer 5

@paki might want to check your arithmetic...

Answer 6

its weight is 620.5kgs (approx)

Answer 7

@kamal10 has better arithmetic :-)

Answer 8

@whpalmer4 yup at the end line my calculation is wrong it is 620.5kgs :-)

and reason for this is solving many questions at the same time :-)

thanks for making the correction.... and for kamal10 too :-)

Answer 9

620.779 kg would be even closer. Those extra digits of pi make a difference when multiplying by large numbers!

Answer 10

yeah... rite

Answer 11

You think I'm kidding? Look at the volume as I go from using \(\pi \approx 3\) to \(\pi \approx 3.1415926\)

\[\begin{array}{c}
76000 \\
78533.3 \\
79546.7 \\
79572. \\
79584.7 \\
79586.9 \\
79587. \\
79587. \\
\end{array}\]

Answer 12

no, i am not saying this that you are kidding... i really appreciate your nice effort... thanks.. @whpalmer4

Answer 13

thanku everyone :)