Question

A toy is in the shape of cylinder whose volume is 2640 cm^3 and height is 2 cm then find T.S.A of cylinder.​

Answer 1

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

$\green{\tt{\therefore{T.S.A\:of\:cylinder=2883.1637\:cm^{2}}}}$

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

$\green{\underline \bold{Given :}} \\ \tt:\implies Volume \: of \: cylinder = 2640 \: {cm}^{2} \\ \\ \tt: \implies Height \: of \: cylinder = 2 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies T.S.A \: of \: cylinder = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \tt: \implies 2640 = \frac{22}{7} \times {r}^{2} \times 2 \\ \\ \tt: \implies \frac{2640 \times 7}{22 \times 2} = {r}^{2} \\ \\ \tt: \implies {r}^{2} = 420 \\ \\ \tt: \implies r = \sqrt{420} \\ \\ \green{\tt: \implies r \approx 20.45 \: cm} \\ \\ \bold{As \: we \: know \:that} \\ \tt: \implies T.S.A \: of \: cylinder = 2 \pi r(h + r) \\ \\ \tt: \implies T.S.A \: of \: cylinder =2 \times 3.14 \times 20.45(2 + 20.45) \\ \\ \tt: \implies T.S.A\: of \: cylinder =2 \times 3.14 \times 20.45 \times 22.45 \\ \\ \green{\tt: \implies T.S.A \: of \: cylinder =2883.1637 \: {cm}^{2} }$

Answer 2

Answer:

The Total Surface Area of the cylinder is  2883.1637 cm²

Step-by-step explanation:

Given :

Volume = 2640 cm³

Height = 2 cm

To find :

The Total Surface Area of the Cylinder

Solution :

Radius of the cylinder -

⇒ Volume of cylinder = 2πr²h

⇒ 2640 = 2 × 22/7 × r² × 2

⇒ 2640 = 44/7 × r²

⇒ 2640 × 7 = 44 × r²

⇒ 18480/44 = r²

⇒ 420 = r²

⇒ r = √420

⇒ r ≈ 20.45

Radius = 20.45 cm

$\rule{300}{1.5}$

Total Surface area of Cylinder -

⇒ 2πr(h + r)

⇒ 2 × 3.14 × 20.45 × (2 + 20.45)

⇒ 2 × 3.14 × 20.45 × 22.45

⇒ 2 × 3.14 × 459.1025

⇒ 2883.1637 cm²

∴ The Total Surface Area of the cylinder is  2883.1637 cm²