Question

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the volume of a cylinder of a height 15 cmis 2310cm3. find it's curved surface area and total surface area​

Answer 1

Answer:

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TO FIND**==>1)curved surface area.

2)total surface area

$\bf\underline{ here \: \: h = 15cm} \\ \\ \bf\underline{ \: \: \pi = \frac{22}{7} } \\ \\ \bf\underline{r =?} \\ \\ \bf\green{ volume \: of \: cylinder = \pi {r}^{2}h }\\ \\ \bf\ \implies2310 = \frac{22}{7} \times { r}^{2} \times 15 \\ \\ \bf\ \implies {r}^{2} = \frac{2310 \times 7}{22 \times 15} \\ \\ \bf\ \implies {r}^{2} = \frac{1155 \times 7}{11 \times 15} \\ \\ \bf\ \implies {r}^{2} = \frac{105 \times 7}{15} \\ \\ \bf\ \implies \: r = \sqrt{49} \\ \\ \bf\underline{ \bigstar\implies \: r = 7cm \: \bigstar} \\ \\ \\ \bf\red{\underline{ \mapsto: curved \: surface \: area \: of \: cylinder = 2 \pi \: rh }}\\ \\ \bf\ \implies 2 \times \frac{22}{7} \times 7 \times 15 {cm}^{2} \\ \\ \bf\ \implies 2 \times22 \times 15 {cm}^{2} \\ \\ \bf\boxed{ \implies 660 {cm}^{2}} \\ \\ \bf\purple{ \underline{ \underline \hookrightarrow : total \: surface \: are \: of \: cylinder = 2 \pi \: r \:h + 2 \pi \: {r}^{2} }} \\ \\ \bf\ \implies 2 \pi \: r(h + r) \\ \\ \bf\ \implies 2 \times \frac{22}{7} \times 7(15 + 7) {cm}^{2} \\ \\ \bf\ \implies 2 \times 22 \times 22 \: {cm}^{2} \\ \\ \bf\boxed{ \implies 968 \: {cm}^{2} } \\ \\ \large\boxed{ \fcolorbox{orange}{yellow}{hope \: it \: help \: you}}$

Answer 2

Answer:

A≈967.87cm²

h Height

15

cm

V Volume

2310

cm³

Using the formulas

A=2πrh+2πr2

V=πr2h

Solving forA

A=2hπV

h+2V

h=2·15·π·2310

15+2·2310

15≈967.86722cm²