Question

Find the surface area of a cylinder whose perimeter of base 85m and height 12m

Answer 1

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

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

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

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

• According to given question :

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

Answer 2

Given:

• Perimeter of base = 85 m

• Height, h = 12 m

To find out:

Find the surface area of a cylinder.

Formula used:

• Perimeter of base = 2πr
• Surface area of cylinder = 2πr(h+r)

Solution:

Perimeter of base = 2πr

85 = 2πr

r = 85/2π ..................(i)

Now,

Surface area of a cylinder = 2πr(h+r)

= 2π × 85/2π ( 12 + 85/2π)

= 85 (12+85/2π)

= 85 (12+85×7/2×22)

= 85 (12+ 595/44)

= 85 × (12+13.522)

= 85 × 25.522

= 2,169.37 m²