Question

fifty-four solid hemispheres each of diameter 2cm, are melted to form a single sphere. find the radius of the sphere.

Answer 1

volume of one sphere will be V= 4/3 * pie* r^3

Answer 2

54 solid hemisphere=27 spheres
now find the volume of these 27 spheres

Answer 3

so volume of 54 54 solid hemisphere will be...
= 54(4/3)(pi)2^3
= 576 pie

Answer 4

how volume of those hemispheres gets us the radius of the other sphere??

Answer 5

hmmm , easy... just use another formula with little simplification....

Answer 6

and then by doing so, you will need the radius... which is equal to the "vol of single sphere" = "vol of the 54 solid hemisphere"... so put the valuse and solve...

(4/3)(pi)r^3 = 576(pi)
(4/3)r^3 = 576
r^3 = 576(3/4)
r^3 = 144(3)
r^3 = 432
take cube rrot and solve...
r = 7.56 cm

Answer 7

@insa

Answer 8

i think it should
(4/3)(pi)r^3 = 36(pi)
then r=3
u cant take 576pi because its volume of hemisphere and u can't equate it with (4/3)(pi)r^3

Answer 9

okay now i get it thx again :)

Answer 10

pleasure...