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Category: Geometry

Question-175717

Question Number 175717 by ajfour last updated on 05/Sep/22 Answered by mr W last updated on 05/Sep/22 $$\left({R}−{r}\right)^{\mathrm{2}} ={r}^{\mathrm{2}} +\left(\frac{{R}}{\mathrm{2}}+{r}\right)^{\mathrm{2}} \\ $$$${r}^{\mathrm{2}} +\mathrm{3}{Rr}−\frac{\mathrm{3}{R}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{0} \\…

Question-44636

Question Number 44636 by Raj Singh last updated on 02/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 $${join}\:{oB}\:{andOC} \\ $$$$\bigtriangleup{OAB}\:{and}\:{OAC}\: \\ $$$$\left.\mathrm{1}\right){OB}={OC}\:\left({radius}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\…

Question-44621

Question Number 44621 by Tawa1 last updated on 02/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 02/Oct/18 $$\left.{a}\right){sector}\:{area}\:{s}=\frac{\pi{r}^{\mathrm{2}} }{\mathrm{2}\pi}×\theta=\frac{{r}^{\mathrm{2}} \theta}{\mathrm{2}} \\ $$$$\mathrm{132}=\frac{\mathrm{12}×\mathrm{12}}{\mathrm{2}}×\theta \\ $$$$\theta=\frac{\mathrm{132}×\mathrm{2}}{\mathrm{12}×\mathrm{12}}=\frac{\mathrm{11}}{\mathrm{6}} \\ $$$${l}={r}\theta…

a-The-area-of-a-sector-of-a-circle-of-radius-12cm-is-132cm-2-If-the-sector-is-folded-such-that-its-straight-edges-coincide-to-form-a-cone-Find-the-radius-of-the-base-of-the-cone-Take-

Question Number 44548 by Tawa1 last updated on 01/Oct/18 $$\left(\mathrm{a}\right) \\ $$$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\:\mathrm{12cm}\:\mathrm{is}\:\:\mathrm{132cm}^{\mathrm{2}} \:.\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{sector} \\ $$$$\mathrm{is}\:\mathrm{folded}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{straight}\:\mathrm{edges}\:\mathrm{coincide}\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{cone}.\:\mathrm{Find}\:\mathrm{the}\: \\ $$$$\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\:\:\:\left[\:\:\mathrm{Take}\:\:\:\:\pi\:\:=\:\:\frac{\mathrm{22}}{\mathrm{7}}\:\right]\:. \\ $$$$ \\ $$$$\left(\mathrm{b}\right)\:\:\: \\ $$$$\mathrm{A}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{O}\:\mathrm{has}\:\mathrm{radius}\:\mathrm{5cm}.\:\:\mathrm{A}\:\mathrm{chord}\:\mathrm{PQ}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{6cm}\:\mathrm{long}. \\ $$$$\mathrm{caclculate}:…