Question

PLEASE answer this question ​

Answer 1

Answer:

AnswEr :

Radius : Height = 3 : 7

Volume of Cylinder = 1584 cm³

Find Dimensions of Cylinder.

Let the Radius be 3x and, Height be 7x.

• According to the Question Now :

$\begin{lgathered}\implies\sf Volume = 1584~{cm}^{3}$ \\ \\$\implies\sf\pi {r}^{2}h = 1584\:{cm}^{3}$ \\ \\$\implies\sf \dfrac{22}{ \cancel7} \times {(3x)}^{2} \times\cancel7x = 1584 \: {cm}^{3}$ \\ \\$\implies\sf22 \times9 {x}^{2} \times x = 1584 \: {cm}^{3}$\\ \\$\implies\sf22 \times 9 {x}^{3} = 1584 \: {cm}^{3}$\\ \\$\implies\sf {x}^{3} =\cancel\dfrac{1584 \:{cm}^{3} }{22}\times\dfrac{1}{9}$\\$\end{lgathered}$

⟹Volume=1584cm

3

⟹πr

2

h=1584cm

3

⟹

7

22

×(3x)

2

×

7

x=1584cm

3

⟹22×9x

2

×x=1584cm

3

⟹22×9x

3

=1584cm

3

⟹x

3

=

22

1584cm

3

×

9

1

\begin{lgathered}\implies\sf {x}^{3} =\cancel{72\: {cm}^{3}}\times\dfrac{1}{\cancel9}\\\\\implies\sf {x}^{3} = 8 \: {cm}^{3} \\ \\\implies\sf x = \sqrt[3]{8 \: {cm}^{3}} \\ \\\implies\sf x = \sqrt[3]{2 \:cm \times 2 \:cm \times 2 \:cm} \\ \\\implies \green{\sf x = 2\:cm}\end{lgathered}

⟹x

3

=

72cm

3

×

9

1

⟹x

3

=8cm

3

⟹x=

3

8cm

3

⟹x=

3

2cm×2cm×2cm

⟹x=2cm

• D I M E N S I O N S :

↠ Radius = 3x = 3(2 cm) = 6 cm

↠ Height = 7x = 7(2 cm) = 14 cm

⠀

∴ Therefore, Radius and Height of cylinder is 6 cm and 14 cm respectively.