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Category: Geometry

Question-60058

Question Number 60058 by ajfour last updated on 17/May/19 Commented by ajfour last updated on 17/May/19 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{and}\:\mathrm{h}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{volume}\:\mathrm{prism} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{R}. \\ $$ Answered by mr W…

Question-191060

Question Number 191060 by Mingma last updated on 17/Apr/23 Answered by witcher3 last updated on 18/Apr/23 $$\mathrm{BS}=\mathrm{a}\frac{\mathrm{d}}{\mathrm{b}},\mathrm{BR}=\frac{\mathrm{d}}{\mathrm{b}}\mathrm{c} \\ $$$$\mathrm{AP}=\mathrm{c}\frac{\mathrm{d}}{\mathrm{a}},\mathrm{AQ}=\mathrm{b}\frac{\mathrm{d}}{\mathrm{a}} \\ $$$$\mathrm{CM}=\mathrm{a}.\frac{\mathrm{d}}{\mathrm{c}},\mathrm{NC}=\frac{\mathrm{d}}{\mathrm{c}}\mathrm{b} \\ $$$$\mathrm{c}\left(\mathrm{1}−\frac{\mathrm{d}}{\mathrm{a}}\right)=\mathrm{BP},\mathrm{c}\left(\mathrm{1}−\frac{\mathrm{d}}{\mathrm{b}}\right)=\mathrm{RA} \\ $$$$\mathrm{PR}=\mathrm{c}\left(\frac{\mathrm{d}}{\mathrm{a}}+\frac{\mathrm{d}}{\mathrm{b}}−\mathrm{1}\right)…

Question-125384

Question Number 125384 by ajfour last updated on 10/Dec/20 Commented by ajfour last updated on 10/Dec/20 $${The}\:{hemisphere}\:{has}\:{radius}\:\mathrm{2}. \\ $$$${The}\:{outer}\:{circular}\:{base}\:{has}\:{radius} \\ $$$$\mathrm{3}.\:{Find}\:{maximum}\:{side}\:{length}\:{of} \\ $$$${equilateral}\:{triangle}\:{with}\:{vertices} \\ $$$${placed}\:{as}\:{shown}.…

Question-59700

Question Number 59700 by ajfour last updated on 13/May/19 Commented by ajfour last updated on 13/May/19 $$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{overlap}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{quarter}\:\mathrm{circle}\:\mathrm{and}\:\mathrm{semicircle}\:\mathrm{both} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{radius}\:\mathrm{and}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{shown}\:\mathrm{orientation}\:\mathrm{as}\:\mathrm{a}\:\mathrm{percentage} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{quarter}\:\mathrm{circle}\:\mathrm{area}.…