InterviewSolution
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InterviewSolution
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If the height , curved surface area and volume of a right circular cone be h, c and v respectively , then that `3pi vh^3-c^2h^2+9v^2=0`. |
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Answer» Let the radius of base and slant height of the cone be r unit and l unit respecitvely. `therefore l^2=h^2+r^2`....................(1) Again, `v=(1)/(3)pi r^2h` .................(2) and `c=pi r l`................(3) `therefore 3 pi vh^3-c^2h^2+9v^2` `=3pi xx(1)/(3)pi r^2h^3-(pi r l)^2xxh^2+9xx((1)/(3)pi r^2h)^2`[by (2) and (3)]. `=pi^2r^2h^4-pi^2r^2l^2h^2+pi^2r^4h^2` `=pi^2r^2h^4-pi^2r^2(r^2+h^2).h^2+pi^2r^4h^2`[by (1)]. `= pi ^2r^2h^4-pi^2r^4h^2-pi^2r^2h^4+pi^2r^4h^2=0` Hence `3pi vh^3-c^2h^2+9v^2=0` . |
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