Question

A rectangular sheet of paper of length 35 cm and breadth 28 cm is folded in two ways to form
a cylinder. Find the difference in the volumes of cylinders formed.
​

Answer 1

Given

A rectangular sheet of paper of length 35 cm and breadth 28 cm is folded in two ways to form a cylinder.

To find

• The difference in the volumes of cylinders formed.

Solution

$\\\bold\dag\:{\sf{\purple{Length\:of\: rectangular\:sheet}}} =\sf 35 cm$

$\bold\dag\:{\sf{\purple{Breadth\:of\: rectangular\:sheet}}} =\sf 28 cm$

A rectangular sheet is folded in two ways to form a cylinder

$\\\qquad\qquad\bullet\:{\underline{\underline{\sf{\green{First\:way :-}}}}}$

A rectangular sheet is folded along its breadth to form a cylinder

$\\\bold\dag\:{\sf{\blue{Breadth= height\:of\:a\:cylinder}}} =\sf 28 cm$

$\bold\dag\:{\sf{\blue{Length = Circumference\:of\:a\: cylinder}}} =\sf 35 cm$

Let's find out radius of a cylinder

$\\\bullet\:{\underline{\sf{\orange{Circumference\:of\:circle = 2\pi r = Length}}}}$

$\implies\sf 35 = 2 \times \dfrac{22}{7} \times r$

$\implies\sf 35 = \dfrac{44r}{7}$

$\implies\sf 35 = \dfrac{44r}{7}$

$\implies\sf r = \dfrac{35\times 7}{44}$

$\implies\sf r = 5.5cm$

$\therefore{\underline{\boxed{\sf{Radius\:of\:a\: cylinder = 5.5 cm}}}}$

$\qquad$ Volume of cylinder

$\\\implies\sf \pi r^2 h$

$\implies\sf \dfrac{22}{7}\times 5.5 \times 5.5 \times 28$

$\implies\sf 22\times 5.5 \times 5.5 \times 4$

$\implies\sf 2662cm^2$

$\therefore{\underline{\boxed{\sf{Volume\:of\:a\: cylinder(V_1) = 2662 cm^3}}}}$

$\:$____________________________________________

$\\\qquad\qquad\bullet\:{\underline{\underline{\sf{\green{Second\:way :-}}}}}$

A rectangular sheet is folded along its length to form a cylinder

$\\\bold\dag\:{\sf{\blue{Length= height\:of\:a\:cylinder}}} =\sf 35 cm$

$\bold\dag\:{\sf{\blue{Breadth = Circumference\:of\:a\: cylinder}}} =\sf 28cm$

Let's find out radius of a cylinder

$\\\bullet\:{\underline{\sf{\orange{Circumference\:of\:circle = 2\pi r = Breadth}}}}$

$\implies\sf 28 = 2 \times \dfrac{22}{7} \times r$

$\implies\sf \cancel\dfrac{28}{2} = \dfrac{22r}{7}$

$\implies\sf 14 = \dfrac{22r}{7}$

$\implies\sf r = \dfrac{14\times 7}{22}$

$\implies\sf r = 4.4cm$

$\therefore{\underline{\boxed{\sf{Radius\:of\:a\: cylinder = 4.4 cm}}}}$

$\qquad$Volume of cylinder

$\\\implies\sf \pi r^2 h$

$\implies\sf \dfrac{22}{7}\times 4.4 \times 4.4 \times 35$

$\implies\sf 22\times 4.4 \times 4.4 \times 5$

$\implies\sf 2129.6cm^2$

$\therefore{\underline{\boxed{\sf{Volume\:of\:a\: cylinder(V_2) = 2129.6 cm^3}}}}$

Difference between the volumes of cylinder formed

$\\\implies\sf V_1 - V_2$

$\implies\sf 2662 - 2129.6$

$\implies\sf 532.4 cm^3$

$\therefore{\underline{\boxed{\sf{Difference\:between\:in\:the\: volumes= 532.4 cm^3}}}}$

$\:$____________________________________________

Answer 2

Answer:

Given :-

A rectangular sheet of paper of length 35 cm and breadth 28 cm is folded in two ways to form a cylinder.

To Find :-

Difference between volume

Solution :-

At first

Way 1

Let's take height as breadth and Length as circumference

35 = 2 × 22/7 × r

35 × 7 = 2 × 22 × r

245 = 44r

245/44 = r

4.5 cm ≈ r

Now,

Volume = πr²h

Volume = 22/7 × 5.5² × 28

Volume = 22/7 × 30.25 × 28

Volume = 22 × 30.25 × 4

Volume = 2662 cm²

Way 2

Lets take Length as height and Breadth as circumference

28 = 2 × 22/7 × r

28/2 = 22/7 × r

14 = 22/7 × r

14 × 7/22 = r

4.4 = r

Now,

Volume = πr²h

Volume = 22/7 × 4.4² × 35

Volume = 22/7 × 19.36 × 35

Volume = 22 × 19.36 × 5

Volume = 2130 cm²

Now,

Difference = 2662 - 2130

Difference = 532 cm

Formula Used Here :-

$\large \sf Circumference = 2 \pi r$

$\large \sf Volume = \pi {r}^{2} h$

$\large \sf Difference = V_1 - V_2$

Know More :-

Area of Circle = πr²

TSA of cuboid = 2(lb + bh + lh)

CSA of cuboid = 2h(l + b)