Question Number 6880 by Tawakalitu. last updated on 01/Aug/16 $${A}\:{cone}\:{of}\:{height}\:\mathrm{10}\:{cm}\:{and}\:{base}\:{radius}\:\mathrm{3}\:{cm}\:{is}\:{held}\:{vertex}\: \\ $$$${down}\:{and}\:{is}\:{filled}\:{with}\:{sand}\:.\:{A}\:{hole}\:{in}\:{the}\:{bottom}\:{of}\:{the}\:{cone} \\ $$$${allows}\:{the}\:{sand}\:{to}\:{escape}\:{at}\:{a}\:{steady}\:{rate}\:{of}\:\mathrm{0}.\mathrm{5}\:{cm}^{\mathrm{3}} /{s}.\:{find}\:{the} \\ $$$${rate}\:{that}\:{the}\:{depth}\:{is}\:{decreasing}\:{when}\:{the}\:{depth}\:{is}\:\mathrm{2}\:{cm}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 72414 by aliesam last updated on 28/Oct/19 Commented by aliesam last updated on 28/Oct/19 $${a},{b}\:{and}\:{d}\:{are}\:{centres}\:{of}\:{three}\:{circles}\: \\ $$$${find}\: \\ $$$$\frac{{AC}}{{AB}} \\ $$ Answered by…
Question Number 6810 by Tawakalitu. last updated on 28/Jul/16 $${Up}\:{to}\:{which}\:{prime}\:{number}\:{should}\:\:\:\mathrm{9}\:\:\:{divide}\:\:\:\mathrm{9631}\:\:\:{to}\:{ensure}\:{that} \\ $$$${this}\:{number}\:{is}\:{a}\:{prime}\:{number}\:{or}\:{a}\:{composite}\:{number}\:? \\ $$ Commented by Rasheed Soomro last updated on 29/Jul/16 $$\mathrm{97} \\ $$$${The}\:{largest}\:{prime}\:{number}\:{not}\:{greater}\:{than}\:\sqrt{\mathrm{9631}}…
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Question Number 6430 by sanusihammed last updated on 27/Jun/16 $${An}\:{oil}\:{can}\:{is}\:{to}\:{be}\:{made}\:{in}\:{form}\:{of}\:{a}\:{right}\:{circular}\:{cylinder}\:{that}\:{be} \\ $$$${inscribed}\:{in}\:{a}\:{sphere}\:{of}\:{radius}\:{R}.\:{obtain}\:{the}\:{maximum}\: \\ $$$${volume}\:{of}\:{the}\:{can}. \\ $$ Commented by sanusihammed last updated on 27/Jun/16 $${Thanks}\:{so}\:{much}\:{sir}.\: \\…
Question Number 6334 by sanusihammed last updated on 24/Jun/16 Commented by nburiburu last updated on 24/Jun/16 $${basically}\:{you}\:\:{need}\:{to}\:{find}\:{first}\:{the}\:{common}\:{area}. \\ $$$${To}\:{do}\:{it},\:{let}\:{be}\:{M}\:{and}\:{N}\:{the}\:{intersection}\:{of}\:{both}\:{circles}\:{and}\:{O}\:{and}\:{P}\:\:{the}\:{centres}\:{of}\:{circle}\:{with}\:{radius}\:{b}\:{and}\:{a}\:,\:{respectively}. \\ $$$${the}\:{area}\:{couldbefound}\:{doing} \\ $$$${Area}.{circ}.{sector}\:\left({NOM}\right)\:+\:{Area}.{circ}.{sector}\:\left({MPO}\right)+{Area}.{circ}.{sector}\left({OPN}\right)\:−\:{Area}\bigtriangleup{MPO}\:−\:{Area}\bigtriangleup{OPN} \\ $$$${and}\:{for}\:{this}\:{is}\:{necessary}\:{to}\:{know}\:{two}\:\:{central}\:{angles}…
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Question Number 6135 by sanusihammed last updated on 15/Jun/16 $${Of}\:{all}\:{rectangular}\:{boxes}\:{without}\:{a}\:{lid}\:{and}\:{having}\:{a}\:{given}\: \\ $$$${surface}\:{area}\:.\:{Find}\:{the}\:{one}\:{with}\:{maximum}\:{volume}. \\ $$ Commented by FilupSmith last updated on 15/Jun/16 $$\mathrm{Edge}\:\mathrm{lengths}\:{a},\:{b},\:{c} \\ $$$$\mathrm{Max}\:\mathrm{volume}\:\mathrm{when}\:{a}={b}={c} \\…
Question Number 6136 by sanusihammed last updated on 15/Jun/16 $${Show}\:{that}\:{of}\:{all}\:{rectangles}\:{inscribed}\:{in}\:{a}\:{given}\:{circle}\: \\ $$$${the}\:{square}\:{has}\:{a}\:{maximum}\:{area}. \\ $$ Answered by Rasheed Soomro last updated on 15/Jun/16 $${All}\:{the}\:{rectangles}\:{inscribed}\:{in}\:{same}\:{circle} \\ $$$${have}\:{equal}\:{diagonals}\:{and}\:{vice}\:{versa}.…
Question Number 5940 by sanusihammed last updated on 05/Jun/16 Answered by FilupSmith last updated on 06/Jun/16 $${Are}\:{of}\:{non}\:{shaded}: \\ $$$${A}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right) \\ $$$$\therefore\mathrm{Total}\:\mathrm{A}{rea}: \\ $$$${A}=\pi{r}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{r}\left(\theta−\mathrm{sin}\:\theta\right)…