Question

(28) Find the surface area of a cylinder whose perimeter of the base 85 m and height 12 m.
​

Answer 1

Answer:

Answer:

\green{\tt{\therefore{T.S.A\:of\:cylinder=2170.475\:cm^{2}}}}∴T.S.Aofcylinder=2170.475cm

2

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

Step−by−stepexplanation:

\begin{gathered} \green{\underline \bold{Fiven :}} \\ \tt: \implies Perimeter \: of \: base = 85 \: m \\ \\ \tt: \implies Height \: of \: cylinder = 12 \: m \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies T.S.A \: of \: cylinder = ?\end{gathered}

Fiven:

:⟹Perimeterofbase=85m

:⟹Heightofcylinder=12m

ToFind:

:⟹T.S.Aofcylinder=?

• According to given question :

\begin{gathered} \bold{As \: we \: know \: that} \\ \tt: \implies Perimeter \: of \: base = 2\pi r \\ \\ \tt: \implies 85 = 2\pi r \\ \\ \tt: \implies \frac{85}{2\pi} = r \\ \\ \tt: \implies r = \frac{85}{2\pi} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies T.S.A \: of \: cylinder = 2\pi r(h + r) \\ \\ \tt: \implies T.S.A \: of \: cylinder = 2\pi \times \frac{85}{2\pi} (12 + \frac{85}{2\pi)} \\ \\ \tt: \implies T.S.A \: of \: cylinder = 85 \times (12 + \frac{85 }{2 \times 3.14 }) \\ \\ \tt: \implies T.S.A \: of \: cylinder = 85 \times (12 + 13.535) \\ \\ \tt: \implies T.S.A \: of \: cylinder = 85 \times 25.535 \\ \\ \green{\tt: \implies T.S.A \: of \: cylinder = 2170.475 \: {cm}^{2} }\end{gathered}

Asweknowthat

:⟹Perimeterofbase=2πr

:⟹85=2πr

:⟹

2π

85

=r

:⟹r=

2π

85

Asweknowthat

:⟹T.S.Aofcylinder=2πr(h+r)

:⟹T.S.Aofcylinder=2π×

2π

85

(12+

2π)

85

:⟹T.S.Aofcylinder=85×(12+

2×3.14

85

)

:⟹T.S.Aofcylinder=85×(12+13.535)

:⟹T.S.Aofcylinder=85×25.535

:⟹T.S.Aofcylinder=2170.475cm

2