Question

A rectangular piece of paper 11cm × 4cm is folded without overlapping to make a cylinder of hieght 4cm. find the volume of the cylinder?​

Answer 1

Answer:

$\small{\boxed{\bold {The\:volume\:of \:cylinder\:is\:38.5cm^3}}}$

$\tt{Given}\begin{cases}\tt{11cm} \\ \tt{4cm} \\\tt{4cm}\end{cases}$

$\large\underline\textsf{To find }$

$\small\textsf{the volume of the cylinder }$

$\large\underline\textsf{Suppose:- }$

$\large\bf{ Radius \:of \:cylinder =\red R}$

$\large\bf{And \:Hieght =\red H}$

$\huge\underline\textsf{Explantion:- }$

$\implies\sf perimeter \: of \: the \: base \: of \: the \: cylinder = 2\pi \: r = 11$

$\implies\sf2 \times \frac{22}{7} \times r = 11$

$\implies\sf r = \frac{7}{4} cm$

$\implies\sf volume \: of \: cylinder = v = \pi \: r {}^{2} h$

$\implies\sf \frac{22}{7} \times \frac{7}{4} \times \frac{7}{4} \times 4cm {}^{3}$

$\leadsto\bf38.5cm {}^{3}$

Answer 2

Step-by-step explanation:

Length of the rectangular piece = 11cm

Breadth of the rectangular piece = 4cm

Since, rectangle is rolled along its width to make cylinder

Height of the cylinder = Width of the rectangular piece = 4cm

Let r be the radius of the cylinder

Now, since rectangular piece is rolled to become cylinder

Therefore, Perimeter of bottom of the cylinder = Length of the rectangular piece

Circumference of circle = 11cm

So, 2πr = 11

2×22/7×r = 11

44/7 ×r = 11×7/44 = 7/4cm

Now,

Volume of the cylinder = πr²h

=> 22/7×(7/4)²×4

=> 22/7×7/4×7/4×4

=> 77/2 => 38.5cm³

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