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Category: Mensuration

Question-19964

Question Number 19964 by ajfour last updated on 19/Aug/17 Commented by ajfour last updated on 19/Aug/17 $${Inscribed}\:{in}\:{a}\:{right}\:{circular}\:{cone} \\ $$$${is}\:{a}\:{sphere}\:{whose}\:{surface}\:{area}\:{is} \\ $$$${equal}\:{to}\:{the}\:{area}\:{of}\:{the}\:{base}\:{if}\:{the} \\ $$$${cone}.\:{In}\:{what}\:{ratio}\:{is}\:{the}\:{lateral} \\ $$$${side}\:{of}\:{the}\:{cone}\:{divided}\:{by}\:{the}\:{line}…

A-circle-is-inscribed-in-an-isosceles-trapezium-Prove-that-the-ratio-of-the-area-of-the-circle-to-the-area-of-the-trapezium-is-equal-to-the-ratio-of-the-circum-ference-of-the-circle-to-the-perimete

Question Number 19940 by ajfour last updated on 18/Aug/17 $${A}\:{circle}\:{is}\:{inscribed}\:{in}\:{an} \\ $$$${isosceles}\:{trapezium}.\:{Prove}\:{that} \\ $$$${the}\:{ratio}\:{of}\:{the}\:{area}\:{of}\:{the}\:{circle} \\ $$$${to}\:{the}\:{area}\:{of}\:{the}\:{trapezium}\:{is} \\ $$$${equal}\:{to}\:{the}\:{ratio}\:{of}\:{the}\:{circum}- \\ $$$${ference}\:{of}\:{the}\:{circle}\:{to}\:{the}\: \\ $$$${perimeter}\:{of}\:{the}\:{trapezium}. \\ $$ Commented…

Question-19915

Question Number 19915 by ajfour last updated on 18/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Four}\:{equal}\:{spheres}\:{of}\:{radius}\:{r} \\ $$$${are}\:{externally}\:{tangent}\:{to}\:{the}\:{three} \\ $$$${others}.\:{Find}\:{the}\:{radius}\:{of}\:{a}\:{sphere} \\ $$$${tangent}\:{to}\:{all}\:{four}\:{spheres}\:{and} \\ $$$${containing}\:{them}\:{within}\:{it}.…

Question-19912

Question Number 19912 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 18/Aug/17 $${Find}\:{tangent}\:{of}\:{the}\:{acute}\:{angle} \\ $$$${between}\:{AB}\:{and}\:{SC}\:{and}\:{the} \\ $$$${shortest}\:{distance}\:{between}\:{them}. \\ $$$${The}\:{side}\:{of}\:{the}\:{equilateral}\:{triangle} \\ $$$${is}\:{even}\:\boldsymbol{{a}}.\:{SA}\:{is}\:{perpendicular}\:{to}…

Question-19736

Question Number 19736 by ajfour last updated on 15/Aug/17 Commented by ajfour last updated on 15/Aug/17 $$\mathrm{Q}.\mathrm{19699}\:\:\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{Find}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{R}\:\left(=\mathrm{100}\right) \\ $$$$\angle\mathrm{OXY}=\mathrm{30}°\:. \\ $$ Answered by…

Question-19675

Question Number 19675 by ajfour last updated on 14/Aug/17 Commented by ajfour last updated on 14/Aug/17 $$\mathrm{Q}.\mathrm{19668}\:\mathrm{Find}\:\mathrm{r}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{side}\:\boldsymbol{\mathrm{d}} \\ $$$$\mathrm{of}\:\mathrm{equilareral}\:\bigtriangleup\mathrm{ABC}\:. \\ $$ Answered by ajfour last…