Question

A sheet of paper 44 cm x 14 cm is rolled to form a cylinder in two different ways. Find the volume
of the cylinder if :
(a) sheet is rolled lengthwise
(b) sheet is rolled breadthwise.​

Answer 1

Step-by-step explanation:

Length = 44cm

Breadth = 14cm

If cylinder is rolled lengthwise then the circumference = 44cm

Circumference = 2πr

$44 = 2 \times \frac{22}{7} \times r \\ r = \frac{44 \times 7}{22 \times 2} = 7$

So, radius = 7cm

Volume of cylinder = πr²h

$= \frac{22}{7} \times 7 \times 7 \times 14 \\ = 22 \times 7 \times 14 = 2156 {cm}^{3}$

If cylinder is rolled breadthwise then circumference becomes 14cm

$14 = 2\pi \: r \\ 14 = 2 \times \frac{22}{7} \times r \\ r = \frac{14 \times 7}{22 \times 2} = \frac{49}{22}$

Volume of cylinder = πr²h

$= \frac{22}{7} \times \frac{49}{22} \times \frac{49}{22} \times 44 \\ = 7 \times 49 \times 2 = 686 {cm}^{3}$

Answer 2

Answer:

length =44cm

breath=14cif cylinder is old length wise then the circumference=44cm

circumference= 2πr

44=2*22/7*r

r=44*7/2*22 (reciprocal)

radius=7

volume of radius= pi r square h

22/7*49*14=154*14=2156cm

Breath=14=2pir

r=14*7/44=49/22

Volume of cylinder,=pi r square h

22/7*49*49/22*22

=14*49=686cm