Question

a rectangular piece of paper is 22 cm in lenght and 10cm in width it is rolled into a cylinder along its lenght find surface area of cylinder ​

Answer 1

According to the question l= 22, b=10..
now this rectangle is rolled into a cylinder with height= 22cm
therefore the breadth become the perimeter of base of the cylinder
2πr=2*22/7*r=10,.... r=10*7/2*22= 35/22
curved surface area of cylinder = 2πrh
= 2*22/7*3 5/22*22
= 220cm2
total surface area = csa of cylinder + area of 2 circles
=220+ 2 ( πr²)
= 220+ 2 ( 22/7*35/22)
= 220+ 2( 5)
=220+10
=230 cm²

Answer 2

Given ,

Rectangle Length=22 cm

Rectangle Width=10 cm

Now when it Roll along with Length.It will form a cylindrical shape.Having

CIRCUMFERANCE=10 cm

Height=22 cm.

(Refer to Fig 1 and Fig 2)

Now Circumference=2πrh

Means

2πr=10 cm. ( π=22/7)

$2 \times \frac{22}{7} \times radius = 10 \\ \\ radius = 2×5\times \frac{7}{22 \times 2} \\ \\radius = 5 \times \frac{7}{22} \\ \\radius = \frac{35}{22} \: cm$

We get Height=22 cm

Radius=$\frac{35}{22} cm$

Curved Surface Area

=2πrh

$2 \times \frac{22}{7} \times \frac{ 7\times5 }{22}\times22 \\ \\ = 2 \times 22 \times 5 \\ = 220 \: {cm}^{2}$

Total Surface Area

=2πr(r+h)

$2 \times \frac{22}{7} \times \frac{7\times5 }{22} ( \frac{35} {22} + 22) \\ \\ = 2 \times 5( \frac{35}{22} + 22) \\ \\ 10( \frac{35}{22} + 22) \\ \\ 10( \frac{35 + 22 \times 22}{22} ) \\ \\ 10( \frac{35 + 484}{22} ) \\ = 10( \frac{519}{22} ) \\ = 235.9$

Approx=236 cm

We get

$\red{\boxed{\mathbf{CSA={220}\:cm^{2}}}}$

$\red{\boxed{\mathbf{TSA={236}\:cm^{2}}}}$