The slant height of the frustum of a cone is 5 cm.

Question:

The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.

Solution:

Slant height of the Frustum = 5 cm

i.e. $l=5 \mathrm{~cm}$.

$r_{1}-r_{2}=4 \mathrm{~cm}$

 

$l=\sqrt{h^{2}+\left(r_{1}-r_{2}\right)^{2}}$

 

$5=\sqrt{h^{2}+(4)^{2}}$

Squaring both sides we get

$25=h^{2}+4^{2}$

$25=h^{2}+16$

$25-16=4^{2}$'

or $h^{2}=9 \mathrm{~cm}$

$4=3 \mathrm{~cm}$

Height of the Frustum = 3 cm

$r_{1}-r_{2}=4 \mathrm{~cm}$

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