Question

What is the height of a cone when slant height is 34 and base diameter is 32?

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\blue{\:\:\:\:\:Given:-\:\:\:\:}}$

$\sf \bullet slant\: height\:of\: cone(l)=34unit\\ \\ \sf \bullet radius =\dfrac{32}{2}= 16unit$

• Now by taking of

Pythagoras formula

$\boxed{\sf{Hypotenuse {}^{2}=base{}^{2}+perpendicular {}^{2}}}$

$\sf l{}^{2}=h{}^{2}+r{}^{2}\\ \\ \sf\implies (34){}^{2}=(16){}^{2}+h{}^{2}\\ \\ \sf\implies 1156=256+h{}^{2}\\ \\ \sf\implies 1156-256=h{}^{2}\\ \\ \sf\implies 900=h{}^{2}\\ \\ \sf\implies \sqrt{900}=h\\ \\ \sf\implies h=30unit$

• The height of cone is

$\boxed{\sf{\blue{Height=30unit}}}$