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

Answer:

• Total surface area of cylinder is 146.08 cm².

Step-by-step explanation:

Given :

• Curved surface area of cylinder is 96.8 cm².
• Height of cylinder is 5.5 cm.

To find :

• Total surface area of cylinder..

Solution :

• Here, We don't have radius for finding total surface area. We will use curved surface area of cylinder for finding radius.

So,

Curved surface area = 2πrh

[Where, r is radius and h is Height of cylinder]

Put height and curved surface area in formula:

$\longrightarrow$ 2 × 22/7 × r × 5.5 = 96.8

$\longrightarrow$ 44/7 × r = 96.8/5.5

$\longrightarrow$ 44/7 × r = 17.6

$\longrightarrow$ 44 × r = 17.6 × 7

$\longrightarrow$ 44 × r = 123.2

$\longrightarrow$ r = 123.2/44

$\longrightarrow$ r = 2.8

Radius of cylinder is 2.8 cm.

Now,

Total surface area = 2πrh + 2πr²

• 2πrh = 96.8 cm² and r is 2.8 cm.

$\longrightarrow$ 96.8 + 2 × 22/7 × (2.8)²

$\longrightarrow$ 96.8 + 44/7 × 7.84

$\longrightarrow$ 96.8 + 344.96/7

$\longrightarrow$ 96.8 + 49.28

$\longrightarrow$ 146.08

∴ Total surface area of cylinder is 146.08 cm².

Answer 2

Answer:

Given :-

CSA of cylinder = 96.8 cm²

Height = 5.5 cm

To Find :-

TSA

Solution :-

CSA = 2πrh

$\sf \: 96.8 = 2 \times \dfrac{22}{7} \times r \times \dfrac{55}{10}$

$\sf \: 96 .8 = \dfrac{22}{7} \times \: r \times \dfrac{55}{5}$

$\sf \: 96.8 = \dfrac{22}{7} \times 11 \times r$

$\sf \: 96 .8\times 7 = 22 \times 11r$

$\sf \: 677.6 = 242r$

$\sf \dfrac{677.6}{242} = r$

$\sf \: 2.8 = r$

Finding TSA

TSA = 2πr(r + h)

$\sf \: 2 \times \dfrac{22}{7} \times 2.8(2.8 + 5.5)$

$\sf \: 44 \times 0.4(2.8 + 5.5)$

$\sf \: 44 \times 0.4(8.3)$

$\sf \: 17.6\times 8.3$

$\sf \: 146 {cm}^{2}$