Question

inner and Outer radii of a pipe are 3 cm and 3.5 CM respectively if the length of pipe is is 8 cm find total surface area​

Answer 1

QUESTION

inner and Outer radii of a pipe are 3 cm and 3.5 CM respectively if the length of pipe is is 8 cm find total surface area

GIVEN

inner radius =3cm

outer radius =3.5cm

FIND

find total surface area =?

ANSWER

$\large \sf 347.27cm^2$

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ㅤㅤㅤㅤㅤㅤㅤㅤEXPLANATION

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Inner surface area =2πrh

$\: \: \: \: \: \: \: \: \: \implies 2 \times \frac{22}{7} \times 3\times 8$

$\: \: \: \: \: \: \: \: \: \implies \frac{44}{7} \times 24$

$\: \: \: \: \: \: \: \: \: \implies 150.85 {cm}^{2}$

Outer surface area =2πrh

$\: \: \: \: \: \: \: \: \: \implies 2 \times \frac{22}{7} \times 3.5\times 8$

$\: \: \: \: \: \: \: \: \: \implies \frac{44}{7} \times 28$

$\: \: \: \: \: \: \: \: \: \implies44 \times 4$

$\: \: \: \: \: \: \: \: \: \implies 176 {cm}^{2}$

Area of top and bottom circle -

$\: \: \: \: \: \: \: \: \: \: \implies 2\times \pi (r_{1}^2-r_{2})\\\\ \: \: \: \: \: \: \: \: \: \: \implies 2 \times \frac{22}{7}(3.5^{2}-3^{2})\\\\ \: \: \: \: \: \: \: \: \: \: \implies \frac{44}{7} \times (12.25 - 9)\\\\ \: \: \: \: \: \: \: \: \: \: \implies \frac{44}{7}\times 3.25\\\\ \: \: \: \: \: \: \: \: \: \: \implies 20.42 cm^2$

Total surface area =Add all the areas

$\: \: \: \: \: \: \: \: \: \implies 150.85 + 176+ 20.42$

$\: \: \: \: \: \: \: \: \: \implies 347.27 {cm}^{2}$

Answer 2

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

$\green{\tt{\therefore{T.S.A \: of \: pipe =347.3 { \: cm}^{2}}}}$

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

$\green{\underline{\bold{Given :}}} \\ \tt: \implies Outer \: radii (r_{2})= 3.5 \: cm \\ \\ \tt: \implies Inner \: radii (r_{1})= 3 \: cm \\ \\ \tt: \implies Height \: of \: pipe(h) = 8 \: cm \\ \\ \red{\underline{\bold{To \: Find :}}} \\ \tt: \implies Total \: surface \: area \: of \: pipe = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies C.S.A \: of \: inner \: pipe = 2\pi r_{1}h \\ \\ \tt: \implies C.S.A \: of \: inner \: pipe =2 \times \frac{22}{7} \times 3 \times 8 \\ \\ \tt: \implies C.S.A \: of \: inner \: pipe =150.9 \: {cm}^{2}-----(1) \\ \\ \bold{Again : } \\ \tt: \implies C.S.A \: of \: outer \: pipe =2\pi r_{2}h \\ \\ \tt: \implies C.S.A \: of \: outer \: pipe =2 \times \frac{22}{7} \times 3.5 \times 8 \\ \\ \tt: \implies C.S.A \: of \: outer \: pipe =2 \times 22 \times 0.5 \times 8 \\ \\ \tt: \implies C.S.A \: of \: outer \: pipe =176 \: {cm}^{2} -----(2) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: top \: circle + bottom \: circle = \pi ({ r_{2}}^{2} - r_{1}^{2} ) \\ \\ \tt: \implies Area \: of \: top \: circle + bottom \: circle = 2\times\frac{22}{7} ( {3.5}^{2} - {3}^{2} ) \\ \\ \tt: \implies Area \: of \: top \: circle + bottom \: circle = 2\times\frac{22}{7} \times 3.25 \\ \\ \tt: \implies Area \: of \: top \: circle + bottom \: circle =20.4\: {cm}^{2}-----(3)$

$\bold{For \: total \: surface \: area} \\ \tt: \implies T.S.A \: of \: pipe = (1) + (2) + (3) \\ \\ \tt: \implies T.S.A \: of \: pipe =150.9 + 176 + 20.4 \\ \\ \green{\tt: \implies T.S.A \: of \: pipe =347.3 { \: cm}^{2} }$