plz solve this fast .
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[tex]\bf\dfrac{Volume\: of \:first \:hemisphere}{Volume \:of\: second\: hemisphere}[/tex] = [tex]\bf\dfrac{8}{27}[/tex]
[tex]\implies[/tex] [tex]\bf\dfrac{(4/3) π r³}{(4/3) π R³}[/tex] = [tex]\bf\dfrac{8}{27}[/tex]
[tex]\implies[/tex] [tex]\bf\dfrac{r³}{R³}[/tex]= [tex]\bf\dfrac{8}{27}[/tex]
Taking cube roots at both sides,
[tex]\bf\dfrac{r}{R}[/tex] = [tex]\bf\dfrac{2}{3}[/tex]
Ratio of their volumes = 8:27
Volume of hemisphere = ⅔ πr³
Let the radii of the smaller and bigger hemispheres be (r) and (R) respectively.
∵ Volume (smaller) ÷ Volume (bigger) = 8/27,
⇒ ⅔ πr³ ÷ ⅔ πR³ = 8/27
⇒ r³/R³ = 8/27
⇒ (r/R)³ = (2/3)³
⇒ r:R = 2:3.
∴ Ratio of radius of the hemispheres is 2:3.