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​

Answer 1

$\red{\underline{\underline{Answer:-}}}$

$\sf{Height \ of \ frustum \ is \ 3 \ cm}$

$\orange{\underline{\underline{Given:}}}$

$\sf{\implies{Slant \ height(l)=5 \ cm}}$

$\sf{\implies{Difference \ between \ two \ radii}}$

$\sf{(r1-r2=4)}$

$\pink{\underline{\underline{To \ find:}}}$

$\sf{Height(h) \ of \ frustum .}$

$\green{\underline{\underline{Solution:}}}$

$\sf{Slant \ height(l)=\sqrt{h^{2}+(r1-r2)^{2}}}$

$\sf{...formula}$

$\sf{\therefore{5=\sqrt{h^{2}+4^{2}}}}$

$\sf{Squaring \ both \ sides}$

$\sf{25=h^{2}+16}$

$\sf{h^{2}=25-16}$

$\sf{h^{2}=9}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{h=3 \ cm}$

$\sf\purple{\tt{\therefore{Height \ of \ frustum \ is \ 3 \ cm}}}$

Answer 2

$\sf\large\underline\red{Answer:}$

$\rm{The \ height \ of \ the \ frustum \ is :3 cm}$

_________________________________________

$\sf\large\underline\pink{given:}$

$\sf\large\underline{let :}$ $\rm{r \ and \ R \ be \ the \ radii \ of \ the. }$

$\rm{circular \ ends \ of \ the \ frustum \ of \ cone }$

$\rm{difference \ between \ radii }$$R-r =4$ ,

$\rm{slant \ height : }$$l=5$

_________________________________________

$\sf\large\underline\pink{To \ find :}$

$\rm{Height \ of \ the \ frustrum }$

_________________________________________

$\sf\large\underline\blue{solution:}$

we know,

${l}^{2} =( {R- r}^{2} )+ {h}^{2}$

${5 }^{2} = {4}^{2} + {h}^{2}$

${h}^{2} = 25 - 16 = 9$

$h = 3$

$\rm\orange{Thus, \ the \ height \ of \ the \ frustum \ is \ 3cm. }$