Question

If slant height of a cone is $13$ cm and the base radius is $5$ cm, then the height of cone is :

• A. $12cm$
• B. $8cm$
• C. $10cm$
• D. $18cm$

Answer 1

Answer: (A)

$12cm$

Given, Slant height $l=13cm$

and Base radius $r=5cm$.

Now, in $△AOB$,

${AB}^2={AO}^2+{OB}^2$

i.e. $l^2=h^2+r^2$

$\Rightarrow h=\sqrt{l^2-r^2}=\sqrt{{\left(13\right)}^2-{\left(5\right)}^2}$

$\Rightarrow h=\sqrt{169-25}=\sqrt{144}$

$\Rightarrow h=12cm$.

$\therefore$ Height of the cone is $12cm$.

Hence, option $A$ is correct.