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Category: Geometry

Question-68962

Question Number 68962 by ahmadshah last updated on 17/Sep/19 Commented by mr W last updated on 17/Sep/19 $${assume}\:{that}\:{the}\:{volume}\:{of}\:{cone}\:{is}\:\mathrm{1}. \\ $$$${x}={height}\:{of}\:{cone} \\ $$$$\mathrm{1}−\left(\frac{\mathrm{8}}{{x}}\right)^{\mathrm{3}} =\left(\frac{{x}−\mathrm{2}}{{x}}\right)^{\mathrm{3}} \\ $$$${x}^{\mathrm{3}}…

In-the-figure-we-have-7-circles-having-the-same-radius-Determine-the-ratio-between-the-perimeter-of-one-of-the-circle-and-the-perimeter-of-the-gray-region-

Question Number 68930 by Maclaurin Stickker last updated on 17/Sep/19 $$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{we}\:\mathrm{have}\:\mathrm{7}\:\mathrm{circles}\:\mathrm{having} \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{radius}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{ratio} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{and}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gray}\:\mathrm{region}. \\ $$ Commented by Maclaurin Stickker last updated…

In-a-cube-ABCD-EFGH-with-a-side-length-of-4-cm-Point-Q-is-the-middle-of-line-AE-and-point-P-lies-on-the-extension-of-line-AB-so-that-BP-AB-1-2-If-is-the-angle-between-the-QG-line-and-the-PQH

Question Number 134428 by liberty last updated on 03/Mar/21 $$\mathrm{In}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{4}\:\mathrm{cm}.\:\mathrm{Point}\:\mathrm{Q}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{middle}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{point}\:\mathrm{P} \\ $$$$\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{extension}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AB} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{BP}\::\:\mathrm{AB}\:=\:\mathrm{1}\::\:\mathrm{2}.\:\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{QG}\:\mathrm{line}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{PQH}\:\mathrm{plane}\:,\:\mathrm{then}\:\mathrm{sin}\:\theta\:=?\: \\ $$ Answered…