Asked by Liz
A microscopic worm is eating its way around the inside of a spherical apple of radium 6 cm. What is the probability that the worm is with 1 cm if the surface of the apple? (Hint: V=(4/3)Pir^3)
Answers
Answered by
Reiny
volume of whole apple
= (4/3)π(6^3) = 288π cm^3
volume of inner part of apple with radius 5 cm
= (4/3)π(5^3) = 500π/3 cm^3
part of apple within 1 cm of outside
= 288π - 500π/3 = 364π/3
prob(being in outer part of apple)
= (364π/3) / (288π)
= 91/216
or
appr .421
= (4/3)π(6^3) = 288π cm^3
volume of inner part of apple with radius 5 cm
= (4/3)π(5^3) = 500π/3 cm^3
part of apple within 1 cm of outside
= 288π - 500π/3 = 364π/3
prob(being in outer part of apple)
= (364π/3) / (288π)
= 91/216
or
appr .421
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