"The radii of two cones are in the ratio 2:1 and their volumes are equal What is the ratio - Maths - Surface Areas and Volumes

Question

"The radii of two cones are in the ratio 2:1 and their volumes are
equal What is the ratio their heights ?" Experts, I have solved
this question and attached it's image below so could you please
check if it is right ? Thanks a lot for your help

Atul Shaw · Accepted Answer

Solution:Let the radius be r and R ; and heights be h and H; also volume be v and V
Volume of cone=13πr2hv=13πr2hAnd, V=13πR2HGiven, v=V⇒13πr2h=13πR2H⇒hH=R2r2=Rr2=212=41Your solution was correct but had some minor mistake
For such question always take separate variables

"The radii of two cones are in the ratio 2:1 and their volumes are equal. What is the ratio their heights ?" Experts, I have solved this question and attached it's image below so could you please check if it is right ? Thanks a lot for your help.