Question

find the difference between volume of two cylinders obtained by folding a rectangular sheet of paper of dimension 10cm multiple 5cm along with its length and breadth ​

Answer 1

Step-by-step explanation:

Given that: Rectangular sheet of paper of dimension 10 cm × 5 cm

To find: difference between volume of two cylinders obtained by folding a rectangular sheet of paper along with its length and breadth .

Solution:

Case1) Sheet folded along its length:

perimeter of top/ base circle of cylinder= length of sheet

$2\pi \: r = 10 \\ \\ r = \frac{10}{2\pi} \\ \\ r = \frac{5}{\pi} \: cm$

height of cylinder: 5 cm

(see attached figure)

$\boxed{Volume \: of \: cylinder = \pi \: {r}^{2} \: h\:\:{unit}^3 }$

$volume_{length}= \pi \times \frac{5}{\pi} \times \frac{5}{\pi} \times 5 \\ \\ = \frac{125}{\pi} \\ \\ = \frac{125 \times 7}{22} \\ \\volume_{length} = 39.77 \: {cm}^{3} .....eq1$

Case 2: Sheet folded along its width:

perimeter of top/ base circle of cylinder =breadth of sheet

$2\pi \: r = 5 \\ \\ r = \frac{5}{2\pi} \: cm \\ \\ height \: of \: cylinder = 10 \: cm \\ \\ volume_{breadth} = \pi \: {r}^{2} h \\ \\ = \pi \times \frac{5}{2\pi} \times \frac{5}{2\pi} \times 10 \\ \\ = \frac{250 \times 7}{4 \times 22} \\ \\ volume_{breadth} = 19.89 \: {cm}^{3} ......eq2$

Difference of volume of cylinder along its length and it's breadth

$volume_{length} - volume_{breadth} \\ \\ = 39.77 - 19.89 \\ \\ = 19.88 \: {cm}^{3}$

Hope it helps you.

Answer 2

Answer:

Step-by-step explanation:

Case 1

Length = 10 cm

Breadth = 5 cm

When we fold from length side then the circumference of base of cylinder is 10

Circumference of circle = 2 πr

10 cm   = 2 * 22/7 * r

10/2 = 22/7 × r

5 ×7 / 22 = r

1.59 = r

Volume of cylinder = πr²h

=  22/7 × 1.59 ×1.59 × 5

= 39.727

Case 2

When we fold from length side then the circumference of base of cylinder is 5

Circumference of circle = 2 πr

5 cm   = 2 * 22/7 * r

5/2 = 22/7 × r

5 ×7 / 44 = r

0.795 = r

Volume of cylinder = πr²h

=  22/7 × 0.795 ×0.795 × 10

=19.8636

Difference between two cylinder = 39.727 - 19.863

                                                        = 19.864