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Category: Geometry

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}.…

Question-59620

Question Number 59620 by ajfour last updated on 12/May/19 Commented by ajfour last updated on 12/May/19 $$\mathrm{Find}\:\mathrm{dimensions}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{volume} \\ $$$$\mathrm{cylinder}\:\mathrm{inscribed}\:\mathrm{within}\:\mathrm{a}\:\mathrm{hemi}- \\ $$$$\mathrm{sphere}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{R}\:\left(\mathrm{in}\:\mathrm{shown}\:\mathrm{orientation}\right). \\ $$ Commented by…

Question-190644

Question Number 190644 by cherokeesay last updated on 08/Apr/23 Answered by a.lgnaoui last updated on 09/Apr/23 $$\mathrm{Algebrique}\:\mathrm{solution} \\ $$$$\mathrm{CercleC}_{\mathrm{1}} \:\:\mathrm{B}:\mathrm{origine}\:\mathrm{du}\:\mathrm{Ref}\:\mathrm{B}\left(\mathrm{0},\mathrm{0}\right) \\ $$$$\mathrm{et}\:\mathrm{de}\:\mathrm{rayon}\:\mathrm{1}\:\:\:\mathrm{C}_{\mathrm{1}} \left(\mathrm{B},\mathrm{1}\right)\:\left(\:\mathrm{B},\mathrm{E}\right):\mathrm{C}_{\mathrm{1}} \cap\mathrm{C}_{\mathrm{2}} \\…

Question-190615

Question Number 190615 by mr W last updated on 07/Apr/23 Commented by mr W last updated on 08/Apr/23 $$\mathrm{1}.\:{find}\:{ratio}\:\frac{{a}_{\mathrm{1}} }{{a}}=?\:{such}\:{that}\:{the}\:{right} \\ $$$${circular}\:{cone}\:{is}\:{cut}\:{into}\:{two}\:{parts}\: \\ $$$${with}\:{equal}\:{volume}\:{as}\:{shown}. \\…