Please-what-s-TSA-of-a-frustrum-of-a-cone-Any-easy-method-

Question Number 221060 by Tawa11 last updated on 23/May/25

Please what’s TSA of a frustrum of a cone?
Any easy method?

Answered by mr W last updated on 23/May/25

Commented by mr W last updated on 24/May/25

for some reason my answer was deleted. here again: A_(Lateral) =((2πr_1 +2πr_2 )/2)×s=π(r_1 +r_2 )s A_(Top) =πr_1 ^2 A_(Bottom) =πr_2 ^2 ⇒TSA=π(r_1 +r_2 )s+π(r_1 ^2 +r_2 ^2 )

$${for}\:{some}\:{reason}\:{my}\:{answer}\:{was} \\ $$$${deleted}.\:{here}\:{again}: \\ $$$${A}_{{Lateral}} =\frac{\mathrm{2}\pi{r}_{\mathrm{1}} +\mathrm{2}\pi{r}_{\mathrm{2}} }{\mathrm{2}}×{s}=\pi\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right){s} \\ $$$${A}_{{Top}} =\pi{r}_{\mathrm{1}} ^{\mathrm{2}} \\ $$$${A}_{{Bottom}} =\pi{r}_{\mathrm{2}} ^{\mathrm{2}} \\ $$$$\Rightarrow{TSA}=\pi\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right){s}+\pi\left({r}_{\mathrm{1}} ^{\mathrm{2}} +{r}_{\mathrm{2}} ^{\mathrm{2}} \right) \\ $$

Commented by Tawa11 last updated on 23/May/25

$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$

Commented by Tawa11 last updated on 23/May/25

$$\mathrm{So},\:\:\:\:\mathrm{s}\:\:=\:\:\frac{\mathrm{2}\pi\left(\mathrm{r}_{\mathrm{2}} \:−\:\:\mathrm{r}_{\mathrm{1}} \right)}{\theta} \\ $$

Commented by Tawa11 last updated on 24/May/25

Great sir. Please what formular is slant height (s), if I need it.

$$\mathrm{Great}\:\mathrm{sir}. \\ $$$$\mathrm{Please}\:\mathrm{what}\:\mathrm{formular}\:\mathrm{is}\:\mathrm{slant}\:\mathrm{height}\:\left(\mathrm{s}\right), \\ $$$$\mathrm{if}\:\mathrm{I}\:\mathrm{need}\:\mathrm{it}. \\ $$

Commented by mr W last updated on 24/May/25

you should tell what is given and what is to find? in the formula above, r_1 and r_2 are radi from top and bottom circles, s is the slant height. s is given! certainly you can also give height h instead of slant height. you can determine s from r_1 , r_2 and h or determine h from r_1 , r_2 and s. but you can not determine s from r_1 and r_2 only.

$${you}\:{should}\:{tell}\:{what}\:{is}\:{given}\:{and}\: \\ $$$${what}\:{is}\:{to}\:{find}?\:{in}\:{the}\:{formula} \\ $$$${above},\:{r}_{\mathrm{1}} \:{and}\:{r}_{\mathrm{2}} \:{are}\:\:{radi}\:{from}\:{top}\: \\ $$$${and}\:{bottom}\:{circles},\:{s}\:{is}\:{the}\:{slant} \\ $$$${height}.\:{s}\:{is}\:{given}!\:{certainly}\:{you}\:{can} \\ $$$${also}\:{give}\:{height}\:{h}\:{instead}\:{of}\:{slant}\: \\ $$$${height}.\:{you}\:{can}\:{determine}\:{s}\:{from} \\ $$$${r}_{\mathrm{1}} ,\:{r}_{\mathrm{2}} \:{and}\:{h}\:{or}\:{determine}\:{h}\:{from} \\ $$$${r}_{\mathrm{1}} ,\:{r}_{\mathrm{2}} \:{and}\:{s}.\:{but}\:{you}\:{can}\:{not}\:{determine} \\ $$$${s}\:{from}\:{r}_{\mathrm{1}} \:{and}\:{r}_{\mathrm{2}} \:{only}. \\ $$

Commented by Tawa11 last updated on 24/May/25

I understand sir. Thanks for your time sir.

$$\mathrm{I}\:\mathrm{understand}\:\mathrm{sir}. \\ $$$$\mathrm{Thanks}\:\mathrm{for}\:\mathrm{your}\:\mathrm{time}\:\mathrm{sir}. \\ $$

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