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  • 13. The ratio of the heights of two right cones having the same radius of the base is 6:5. Find the ratioof their (a) volumes and (b) curved surface areas, when each radius of the base is half the height ofthe shorter cone.?

13. The ratio of the heights of two right cones having the same radius of the base is 6:5. Find the ratioof their (a) volumes and (b) curved surface areas, when each radius of the base is half the height ofthe shorter cone.?

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Dimension of bigger cone: h_1,l_1,r

Dimension of smaller cone: h_2,l_2,r

frach_1h_2=frac65

a) Ratio; of ; the ; volume ; =fracV_1V_2=fracprod imes r imes h_1prod imes r imes h_2=frach_1h_2=frac65

b)   l_1^2=r^2+h_1^2

      l_1^2=(frach_22)^2+h_1^2 ;;;;;;;;;;;;;;;;; (ecause r=frach_22)

      l_1^2=(frac56 imes2 imes h_1)^2+h_1^2

     l_1=frac1312 imes h_1

     l_2^2=r^2+h_2^2

     l_2^2=(frach_22)^2+h_2^2 ;;;;;;;;;;;;;;;;; (ecause r=frach_22)

    l_2^2=frac54 imes h_2^2

    l_2^2=frac54 imes (frac56 imes h_1)^2

    l_2=frac5 sqrt512 imes h_1

    Ratio; of ; the ; C.S.A.=fracC.S.A._1C.S.A._2=fracprod imes r imes l_1prod imes r imes l_2=fracl_1l_2=frac 1312 imes frac125sqrt5=frac135sqrt5

 

Posted by

Deependra Verma

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