Question

T2. A rectangular piece of paper having
length 4.4 cm and breadth 1.5 cm is to
be rolled along its length to form a right
circular cylinder. Find the height and the
volume of the right circular cylinder.​

Answer 1

Given -

• Length of rectangle = 4.4 cm

• Breadth of rectangle = 1.5cm

To find -

• The height and volume of Cylinder formed.

Formula used -

• Circumference of circle.

• Volume of cylinder.

Solution -

In the question, we are provided with the dimensions of rectangle, And then, it was rolled from the length side to form a cylinder, and we need to find the height and the volume of the cylinder. First we will find the radius of the cylinder by using the circumference of circle formula and then we will find the volume of the cylinder, by using volume of cylinder formula. Let's do it !

So -

As it is given that, the rectangle is rolled from length side of the rectangle, so, the height of the cylinder will be equal to the Length of the cylinder.

$\sf \: length \: of \: rectangle \: = height \: of \: cylinder$

$\sf \: 4.4cm \: = height \: of \: cylinder$

∴ Height of cylinder is 4.4 cm

Now -

For finding the volume of cylinder, we need radius. As the length of the rectangle is equal to the height of cylinder, then the breadth of the rectangle will be equal to the circumference of the cylinder. And from the formula of circumference of the circle, we will find the radius. Here, we will take, π as 3.14!

$\sf \: circumfrence = breadth \: of \: rectangle \sf \longrightarrow\: 2 \: \pi \: r \: = 1.5 \: cm \sf \longrightarrow \: 2 \: \times \: 3.14 \: \times r \: = 1.5 \: \sf \longrightarrow \: 6.28 \: \times r = 1.5 \sf \longrightarrow \: r \: = \dfrac{1.5}{6.28} \\ \sf \longrightarrow \: r \: = 0.238 \: cm$

Now -

We have height and we have radius so, now, we will apply the formula of volume of cylinder, to obtain the same.

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

On substituting the values -

$\sf \: volume \: = 3.14 \: \times {(0.238)}^{2} \times 4.4 \: cm \\\sf \: volume \: = 3.14 \: \times 0.0566 \: \times 4.4 \: cm\\ \sf \: volume \: = 0.1778 \: \times 4.4 \: cm \\\sf \: volume \: = 0.782 \: {cm}^{3}$

∴ The height of cylinder is 4.4 cm and volume is 0.782 cm³

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