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Category: Geometry

Find-the-minimum-surface-area-of-a-solid-circular-cylinder-if-its-volume-is-16pi-cm-3-leave-your-answer-in-terms-of-pi-

Question Number 23133 by tawa tawa last updated on 26/Oct/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{solid}\:\mathrm{circular}\:\mathrm{cylinder}\:,\:\:\mathrm{if}\:\mathrm{its}\:\mathrm{volume}\:\mathrm{is} \\ $$$$\mathrm{16}\pi\:\mathrm{cm}^{\mathrm{3}} \:\:\:\left(\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\pi\right) \\ $$ Answered by ajfour last updated on 26/Oct/17 $${S}=\mathrm{2}\pi{rh}+\mathrm{2}\pi{r}^{\mathrm{2}} \\…

Question-88541

Question Number 88541 by ajfour last updated on 11/Apr/20 Commented by ajfour last updated on 11/Apr/20 $${The}\:{two}\:{shown}\:{spheres},\:{each}\:{of} \\ $$$${radius}\:{r}\:{are}\:{tangent}\:{to}\:{each}\:{other} \\ $$$${and}\:{to}\:{the}\:{faces}\:{of}\:{a}\:{dihedral}\: \\ $$$${angle}\:\alpha.\:{Find}\:{the}\:{radius}\:{of}\:{the} \\ $$$${sphere}\:{that}\:{is}\:{tangent}\:{to}\:{the}…

Consider-the-transformation-f-of-the-plane-with-all-points-M-wity-affix-z-mapped-to-the-point-M-with-affix-z-such-that-z-3-i-z-1-i-1-3-1-Given-M-0-the-point-z-0-3-4-3-4-i-calcu

Question Number 88479 by Ar Brandon last updated on 10/Apr/20 $${Consider}\:{the}\:{transformation}\:\boldsymbol{{f}}\:{of}\:{the}\:{plane}\:{with}\:{all}\:{points} \\ $$$$\boldsymbol{{M}}\:{wity}\:{affix}\:\boldsymbol{{z}}\:{mapped}\:{to}\:{the}\:{point}\:\boldsymbol{{M}}\:'\:{with}\:{affix}\:\boldsymbol{{z}}\:' \\ $$$${such}\:{that}\:\boldsymbol{{z}}\:'=−\left(\sqrt{\mathrm{3}}+{i}\right){z}−\mathrm{1}+{i}\left(\mathrm{1}+\sqrt{\mathrm{3}}\right) \\ $$$$\left.\mathrm{1}\right)\:{Given}\:\boldsymbol{{M}}_{\mathrm{0}} \:{the}\:{point}\:\boldsymbol{{z}}_{\mathrm{0}} =\frac{\sqrt{\mathrm{3}}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{4}}{i} \\ $$$${calculate}\:\boldsymbol{{AM}}_{\mathrm{0}} \:{and}\:{deduce}\:{the}\:{angle}\:{in}\:{radians} \\ $$$$\left({Taking}\:\boldsymbol{{A}}\:{as}\:{the}\:{center}\:{of}\:{the}\:{transformation}\right) \\…