Question

Intr-un pahar de forma cilindrica avand raza bazei r= 40 mm si inaltimea h= 0,1 m,se introduc doua bile identice cu raza r= 2/10^2 m. Sa se afle ce volum de apa trebuie turnat in paharul cu bile pentru a-l umple.

Answer 1

$r=4~cm;~h=10~cm$
$V_{pahar}=\pi r^2h=\pi\cdot4^2\cdot10=160\pi~cm^3$
$r_{bila}=\frac{2}{10^2}~m=2~cm$
$V_{bila}=\frac{4\pi r^3}{3}=\frac{4\pi\cdot2^3}{3}=\frac{32\pi}{3}=10,(6)\pi~cm^3$
$2\cdot V_{bila}=21,(3)\pi~cm^3$
$V_{apa}=160\pi-21,(3)\pi=138,(6)\pi~cm^3$