Question

the radius and height of cylinder are in the ratio 3:7 And the volume of the cylinder is 1584cm³ Write the dimensions of cylinder ​

Answer 1

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 :

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

$\begin{array}{r|l} &\sf 72 \\\cline{1-2} 22& 1\:5\:8\:4\\ &1\:5\:4 \\ \cline{2-2} & \quad\:\:4\:4\\&\quad\:\:4\:4\\\cline{2-2}&\quad\:\boxed{0\:0}\end{array}$

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

$\rule{300}{2}$

• 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.

Answer 2

Answer:

$\large\boxed{\sf{Radius=6\:cm\:,\:Height=14\:cm}}$

Step-by-step explanation:

It's being given that the radius and height of a cylinder are in the ratio 3:7.

Let the radius and height of cylinder are $\sf{'r'}$ and $\sf{'h'}$ respectively.

Therefore, we have the relation,

$\sf{ = > \frac{r}{h} = \frac{3}{7} } \\ \\ \sf{ = > r = \frac{3}{7} h \: \: \: \: \: ..........(1)}$

Also, the volume is $\sf{1584\:{cm}^{3}}$.

Therefore, we have the relation,

$\sf{= > \pi {r}^{2} h = 1584} \\ \\ \sf{ = > \pi {( \frac{3}{7} h)}^{2} h = 1584 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: from \: (1)} \\ \\ \sf{= > {h}^{3} = \frac{1584 \times 49 \times 7}{22 \times 9} } \\ \\ \sf{ = > {h}^{3} = 8 \times 49 \times 7 }\\ \\ \sf{ = > {h}^{3} = {(2 \times 7)}^{3}} \\ \\ \sf{ = > {h}^{3} = {(14)}^{3} } \\ \\ \sf{= > h = 14 \: cm}$

Thus height is 14 cm

Therefore radius will be,

$\sf{= > r = \frac{3}{7} \times 14} \\ \\ \sf{ = > r = 3 \times 2 }\\ \\ \sf{= > r = 6 \: cm}$

Thus radius is 6 cm.