Question

find the total surface area of a cylinder of height 8cm and radius of base 4 cm​

Answer 1

GIVEN :–

• Height of cylinder = 8 cm

• Radius of cylinder = 4 cm

TO FIND :–

• Total surface area of cylinder = ?

SOLUTION :–

• We know that –

$\\ \longrightarrow \large { \boxed{\sf Total \: \: surface \: \: area = 2\pi rh + 2\pi {r}^{2} }}$

• Here –

$\\ \: \: \: \: \: { \huge{.}} \: \sf \: \: r = radius \: \: of \: \: cylinder$

$\\ \: \: \: \: \: { \huge{.}} \: \sf \: \: h = height \: \: of \: \: cylinder$

• Now put the values –

$\\ \implies \sf Total \: \: surface \: \: area = 2\pi rh + 2\pi {r}^{2}$

$\\ \implies \sf Total \: \: surface \: \: area = 2\pi (4)(8) + 2\pi {(4)}^{2}$

$\\ \implies \sf Total \: \: surface \: \: area = 2\pi (32) + 2\pi (16)$

$\\ \implies \sf Total \: \: surface \: \: area = 64\pi + 32\pi$

$\\ \implies \large { \boxed{ \sf Total \: \: surface \: \: area = 96 \: \pi }}$

• Hence , Total surface area is 96 π cm².

Answer 2

Given :-

• Height of the cylinder = 8 cm

• Radius of the cylinder = 4 cm

Required to find :-

• Total Surface Area of the cylinder

Formula used :-

$\text{ TSA of a cylinder } \rm = 2\pi r(r + h)$

Solution :-

Given that :-

• Height of the cylinder = 8 cm

• Radius of the cylinder = 4 cm

We need to find the Total surface area of the cylinder .

In order to find it's TSA we need to use a formula

So,

Using the formula ,

$\text{ TSA of a cylinder } \rm = 2\pi r(r + h)$

By substituting the values ,

We get ,

( Use π = 3.14 )

$\rightarrowtail \rm TSA \: of \:a \: cylinder \: = 2 \times 3.14 \times 4(4 + 8) \\ \\ \rightarrowtail \rm TSA \: of \: a \: cylinder \: = 2 \times 3.14 \times 4(12) \\ \\ \rightarrowtail \rm TSA \: of \: a \: cylinder \: = 8 \times 3.14 \times 12 \\ \\ \rightarrowtail \rm TSA \: of \: a \: cylinder \: = 25.12 \times 12 \\ \\ \rightarrowtail \rm TSA \: of \: a \: cylinder \: = 301.44 \\ \\ \implies \tt TSA \: of \: the \: cylinder \: = 302 {cm}^{2} (approximately)$

Additional Information :-

1. The above answer in the terms of π is 96π cm²

2. The formula related to cylinder are ;

• LSA of a cylinder = 2πrh

• Volume of a cylinder = πr²h