Question

Find the radius of a cylinder whose
Total surface area is 11000 m²
and height is 15m.​

Answer 1

Answer:

TSA = 2Πr(h+r)

11000 = 2×22/7 × r(15+r)

11000= 44/7×r(15+r)

11000×7/44 = 15r+r²

250×7= 15r+r²

1750= 15r +r²

1750/15 = r+r²

110= r+r²

110-r = r²

r = √110-r

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Radius\:of\:cylinder=35\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \text{Height(h) = 15\: m} \\ \\ : \implies \text{T.S.A\:of\:cylinder=}11000 \: m^{2} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Radius\: of \: cylinder(h) = ? }$

• According to given question :

$\bold{As \: we \: know \: that} \\ : \implies \text{T.S.A\: of \: cylinder} =2\pi r(h + r) \\ \\ : \implies 11000=2 \times \frac{22}{7} \times r(15+r) \\ \\ : \implies \frac{77000}{44} =15r+r^{2}$

$: \implies {r}^{2} + 15r - 1750 = 0 \\ \\ : \implies r = \frac{ { - 15 \pm} \sqrt{225 - 4( - 1750)} }{2} \\ \\ : \implies r = \frac{ - 15 \pm \sqrt{225 + 7000} }{2} \\ \\ : \implies r = \frac{ - 15 \pm85}{2} \\ \\ : \implies r = \frac{ - 15 + 85}{2} \\ \\ \green{: \implies \text{r = 35 \: cm}}$

$\purple{\text{Some\:formula\:related\:to\:this\:topic}}\\ \pink{\circ\:\text{Volume\:of\:cylinder}=\pi r^{2}h}\\\\ \pink{\circ\:\text{C.S.A\:of\:cylinder}=2\pi rh}$