Question

A rectangular sheet of paper of dimension 66×15cm is rolled along it's length to form a cylinder of height 15cm. Find the volume of the cylinder.

Answer 1

$\huge\star{\underline{\sf{\red{Answer\implies5197.5cm^{3}}}}}\star$

Given:

• Length of Rectangle = Perimeter of Base of the cylinder= 66 cm

• Breadth of Rectangle = Height of the Cylinder = 15 cm

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$\large\square$To Find:

Volume of the Cylinder

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$\large\square$ Formula

$\large\star$ 2πr = Perimeter of circle

$\large\star$ πr²h = Volume of cylinder

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$\large\square$Solution:

Radius = r

$\implies$ 66 cm= 2πr

$\implies$ r= $\dfrac{66}{2\times \frac{22}{7}}$

$\implies$ r= $\dfrac{\cancel{66}\times 7}{2 \times\cancel{22}}$

$\implies$ r = $\dfrac{3 \times 7}{2}$

$\implies$ r= ${\boxed{\dfrac{21}{2}cm}}$

Now, Volume = πr²h

$\implies$ $\dfrac{22}{7} \times \bigg(\dfrac{21}{2}\bigg)^{2} \times 15$

$\implies$ $\dfrac{22}{\cancel7} \times \dfrac{\cancel{441}}{4} \times 15$

$\implies$$11 \times \dfrac{63}{2} \times15$

$\implies$ $11 \times 31.5 \times 15$

$\implies$ $\large{\boxed{\boxed{5197.5cm^{3}}}}$

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Answer 2

$\huge \red{\mathfrak{solution}}$

Given:

• Length of the rectangular sheet = 66cm

• breadth of the rectangular sheet= 15cm

As we know that :

◆ Length of rectangular sheet = circumference of the circle

$\rightarrow \: 66 = 2 \: \pi \: r \\ \\ \rightarrow \: r = \frac{66}{2 \times \frac{22}{7} } \\ \\ \rightarrow \: r = \frac{66 \times 7}{22 \times 2} \\ \\ \rightarrow \: r = \frac{21}{2} = 10.5$

•radius = 21/2 cm = 10.5cm

and

• height =15cm

◆ Volume of cylinder =

$\huge \green{\boxed{\pi \: {r}^{2} h}}$

Now put the values :

$\leadsto \: \frac{22}{7} \times 10.5 \times 10.5 \times 15 \\ \\ \leadsto \frac{22 \times 1653.75}{7} \\ \\ \leadsto \: \frac{36382.5}{7} \\ \\ \leadsto \: 5197.5$

Hence , the volume of cylinder is

$\pink{ \bold{\boxed{5197.5 \: {cm}^{3} }}}$