Question Number 44548 by Tawa1 last updated on 01/Oct/18
![(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 π = ((22)/7) ] . (b) A circle of centre O has radius 5cm. A chord PQ of the circle is 6cm long. caclculate: (i) The distance of the chord from the centre O (ii) The angle POQ](Q44548.png)
$$\left(\mathrm{a}\right) \\ $$$$\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\:\mathrm{12cm}\:\mathrm{is}\:\:\mathrm{132cm}^{\mathrm{2}} \:.\:\:\mathrm{If}\:\mathrm{the}\:\mathrm{sector} \\ $$$$\mathrm{is}\:\mathrm{folded}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{straight}\:\mathrm{edges}\:\mathrm{coincide}\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{cone}.\:\mathrm{Find}\:\mathrm{the}\: \\ $$$$\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\:\:\:\left[\:\:\mathrm{Take}\:\:\:\:\pi\:\:=\:\:\frac{\mathrm{22}}{\mathrm{7}}\:\right]\:. \\ $$$$ \\ $$$$\left(\mathrm{b}\right)\:\:\: \\ $$$$\mathrm{A}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{O}\:\mathrm{has}\:\mathrm{radius}\:\mathrm{5cm}.\:\:\mathrm{A}\:\mathrm{chord}\:\mathrm{PQ}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{6cm}\:\mathrm{long}. \\ $$$$\mathrm{caclculate}: \\ $$$$\:\:\:\:\left(\mathrm{i}\right)\:\:\:\mathrm{The}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{chord}\:\mathrm{from}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{O} \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\:\mathrm{The}\:\mathrm{angle}\:\mathrm{POQ} \\ $$