Question

The circumference of a solid cylinder is 88 cm and its height is 10 cm.
Find
(i) the total surface area,
(ii) the volume
of the cylinder.​

Answer 1

Circumference = 2πr

88 = 2×22/7×r

r = 88×7/44 = 2×7 = 14cm

h = 10cm

TSA = 2πr(r+h)

= 2×22/7×14(14+10)

= 44×2×24 = 2112cm²

Volume = 4/3πr³

= 4/3×22/7×14³ = 11498.67cm³

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Answer 2

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

$\green{\tt{\therefore{T.S.A\:of\:cylinder=2112\:cm^{2}}}}$

$\green{\tt{\therefore{Volume\:of\:cylinder=6160\:cm^{3}}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Circumference \: of \: base \: of \: cylinder = 88 \: cm \\ \\ \tt: \implies Height \: of \: cylinder = 10 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies T.S.A \: of \: cylinder = ? \\ \\ \tt: \implies Volume\: of \: cylinder = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Circumference \: of \: base = 88 \: cm \\ \\ \tt: \implies 2\pi \: r = 88 \\ \\ \tt: \implies r = \frac{88}{2\pi} = 14 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies T.S.A \: of \: cylinder = 2\pi r(h + r) \\ \\ \tt: \implies T.S.A \: of \: cylinder =2 \times \frac{22}{7} \times 14(10 + 14) \\ \\ \tt: \implies T.S.A \: of \: cylinder =88 \times 24 \\ \\ \green{\tt: \implies T.S.A \: of \: cylinder =2112 \: {cm}^{2} } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Volume\: of \: cylinder = \pi {r}^{2}h \\ \\ \tt: \implies Volume\: of \: cylinder = \frac{22}{7} \times {14}^{2} \times 10 \\ \\ \tt: \implies Volume \: of \: cylinder =22 \times 28 \times 10 \\ \\ \green{\tt: \implies Volume \: of \: cylinder =6160 \: {cm}^{3} }$