Question

3. The volume and height of a cylinder are 38.5 cm
and 4 cm respectively. Find the curved surface
area and total surface area of the cylinder.
​

Answer 1

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

$\green{\tt{\therefore{C.S.A\:of\:cylinder=44\:cm^{2}}}}$

$\green{\tt{\therefore{T.S.A\:of\:cylinder=63.25\:cm^{2}}}}$

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

$\green{ \underline \bold{Given:}} \\ \tt:\implies Volume \: of \: cylinder = 38.5 \: {cm}^{3} \\ \\ \tt: \implies Height \: of \: cylinder = 4 \: cm \\ \\ \red{ \underline \bold{To \: Find:}} \\ \tt: \implies C.S.A \: of \: cylinder = ? \\ \\ \tt: \implies T.S.A\: of \: cylinder = ?$

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cylinder = 38.5 \: {cm}^{2} \\ \\ \tt: \implies \pi {r}^{2} h = 38.5 \\ \\ \tt: \implies \frac{22}{7} \times {r}^{2} \times 4 = 38.5 \\ \\ \tt: \implies {r}^{2} = \frac{38.5 \times 7}{22 \times 4} \\ \\ \tt: \implies {r}^{2} = 3.0625 \\ \\ \tt: \implies r = \sqrt{3.0625} \\ \\ \green{\tt: \implies r = 1.75 \: cm} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies \: C.S.A \: of \: cylinder = 2\pi rh \\ \\ \tt: \implies \: C.S.A \: of \: cylinder =2 \times \frac{22}{7 } \times 1.75 \times 4 \\ \\ \tt: \implies \: C.S.A \: of \: cylinder =2 \times22 \times 0.25 \times 4 \\ \\ \green{\tt: \implies \: C.S.A \: of \: cylinder =44 \: {cm}^{2} } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies \: T.S.A \: of \: cylinder = 2\pi r(h + r) \\ \\ \tt: \implies \: T.S.A \: of \: cylinder =2 \times \frac{22}{7 } \times 1.75 (4 + 1.75) \\ \\ \tt: \implies \: T.S.A \: of \: cylinder =2 \times22 \times 0.25 \times 5.75 \\ \\ \green{\tt: \implies \: T.S.A\: of \: cylinder =63.25 \: {cm}^{2} }$

Answer 2

Given :

Volume of cylinder(V) =38.5 cm³

Height of cylinder(h) =4 cm

To Find :

Curved surface area of cylinder =?

Total surface area of cylinder =?

Formula used :

$Curved \: surface \: area = 2\pi rh$

$total \: surface \: area \: = 2\pi r(r + h)$

Solution :

According to the question,

$volume \: = 38.5$

$= > volume \: = \pi {r}^{2} h \\ = > 38.5 = 3.14 \times {r}^{2} \times 4 \\ = > \frac{38.5}{3.14 \times 4} = {r}^{2}$

$= > \sqrt{} 3.06528662 = 1.75(approx) = r$

r =1.75 cm.

Now,

C. S. A of cylinder =2×3.14×1.75×4 cm²

C. S. A of cylinder =44 cm²

And,

T. S. A of cylinder =2×3.14×1.75(1.75+4)

T.S.A of cylinder =63.25 cm²

Therefore the curved surface area of cylinder is 44 cm ² and total surface area of cylinder is 63.25 cm ².