Let S be the area of the slant height of a right circular cone,V the volume , h the height and alpha is the  semi vertical angle then prove that

S=pie×h3×sin alpha/cos2alpha and V=1/3 pie ×h3×tan2alpha

Asked by rushabhjain.a | 1st Dec, 2018, 05:47: PM

Expert Answer:


radius r of the base of the cone is given by,  r = h×tanα
slant height l = begin mathsize 12px style fraction numerator h over denominator cos space alpha end fraction end style
Surface Area S = π × r × l = begin mathsize 12px style pi cross times h cross times tan alpha cross times fraction numerator h over denominator cos alpha end fraction space equals space pi cross times h squared cross times fraction numerator sin alpha over denominator cos squared alpha end fraction end style
Volume V = begin mathsize 12px style 1 third pi space r squared h space equals space 1 third straight pi cross times straight h squared tan squared straight alpha cross times straight h space equals space 1 third straight pi space straight h cubed space tan squared straight alpha end style

Answered by Thiyagarajan K | 1st Dec, 2018, 09:48: PM

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