SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 95 of 100

Marks: +1, -0

The numerical values of the volume and the area of the lateral surface of a right circular cone are equal. If the height of the cone be h and radius be

r,

the value of

{1}/{h^{2}}+ {1}/{r^{2}}

$1/3$
$1/9$
$9/1$
$3/1$

Validate

Solution:

(2) Lateral surface of cone

=\π r √{h^{2}+r^{2}}

Its volume

=1/3\πr^2h

\π r √{h^{2}+r^{2}}= {1}/{3} \π r^{2} h

⇒√{h^{2}+r^{2}}= {r h}/{3}

On squaring both sides,

h^{2}+r^{2}= {r^{2} h^{2}}/{9}

⇒{h^{2}+r^{2}}/{r^{2} h^{2}}= {1}/{9}

⇒{h^{2}}/{r^{2} h^{2}}+ {r^{2}}/{r^{2} h^{2}}= {1}/{9}

⇒{1}/{r^{2}}+ {1}/{h^{2}}= {1}/{9}

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