Question

If the curved surface of a cylinder is 96.8 sq.cm and its height is 5.5 cm then find its total area​

Answer 1

Given :

• The curved surface of a cylinder is 96.8cm².
• Height of Cylinder = 5.5cm

To Find :

• Total Surface Area of Cylinder

Solution :

✰ As we know that, Total Surface Area of Cylinder is given by 2πr (h + r) and in this question Curved Surface Area of Cylinder and height of Cylinder are given, so firstly we will find the radius of the Cylinder and then we will find the Total Surface Area of Cylinder. We will be using the formula of Curved Surface Area of Cylinder (2πrh) to find the radius of the Cylinder.

⠀⠀⠀

⠀⠀⟼⠀⠀CSA of Cylinder = 2πrh

⠀⠀⟼⠀⠀96.8 = 2 × 22/7 × r × 5.5

⠀⠀⟼⠀⠀96.8/2 = 22/7 × r × 5.5

⠀⠀⟼⠀⠀48.4 = 22/7 × r × 5.5

⠀⠀⟼⠀⠀48.4 × 7 = 22 × r × 5.5

⠀⠀⟼⠀⠀338.8 = 22 × r × 5.5

⠀⠀⟼⠀⠀338.8/22 = r × 5.5

⠀⠀⟼⠀⠀15.4 = r × 5.5

⠀⠀⟼⠀⠀15.4/5.5 = r

⠀⠀⟼⠀⠀2.8cm = r

⠀

Now,

⟼⠀⠀TSA of Cylinder = 2πr (h + r)

⟼⠀⠀TSA of Cylinder = 2πr (5.5 + 2.8)

⟼⠀⠀TSA of Cylinder = 2 × π × 2.8 × 8.3

⟼⠀⠀TSA of Cylinder = 2 × 22/7 × 23.24

⟼⠀⠀TSA of Cylinder = 44/7 × 23.24

⟼⠀⠀TSA of Cylinder = 44 × 23.24/7

⟼⠀⠀TSA of Cylinder = 1,022.56/7

⟼⠀⠀TSA of Cylinder = 146.08cm²

Thus Total Surface Area of Cylinder is 146.08cm²

________________

$\small\boxed{\begin{array}{cc}\large \red{\boxed{\sf\dag \: {\underline{Formulae \: Related \: to \: Cylinder :}}}} \\ \\ \bigstar \: \sf Area\:of\:Base\:and\:top =\pi r^2 \\ \\\bigstar \: \sf Curved \: Surface \: Area =2 \pi rh \\ \\ \bigstar \: \sf Total \: Surface \: Area = 2 \pi r(h + r) \\ \\ \bigstar \: \sf Volume=\pi r^2h \end{array}}$

Answer 2

Radius of cylinder (r)=7cm

Height of cylinder (h)=15cm

Curved Surface Area =2πrh

=2×(22/7)×7×15

=660cm/2

Total Surface Area =2πr(h+r)

=2×(22/7)×7(15+7)

=2×22×22

=968cm

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