Question

A cylinder is open at both ends and made of 3 cm thick metal , the external diameter is 24 cm and height is 168 cm. What is the volume of metal used in making the cylinder ? Find the weight of cylinder . If 2 cm cube of the metal weight 15g.​

Answer 1

${\huge{\underbrace{\rm{Question}}}}$

A cylinder is open at both ends and made of 3 cm thick metal , the external diameter is 24 cm and height is 168 cm . What is the volume of metal used in making the cylinder? find the weight of cylinder . If 1 cm cube of the metal weight 15 g.

${\huge{\underbrace{\rm{Answer}}}}$

Given:

• Thickness of the metal is 3 cm
• the external diameter of the cylinder is 24 cm
• Height of the cylinder is = 168 cm

To find:

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• What is the volume of metal used in making the cylinder
• find the weight of cylinder . If 2 cm cube of the metal weight 15 g

Solution:

⠀⠀

• External diameter of the cylinder is 24

External radius of the cylinder is= $\sf{\dfrac{24}{2}}$

$\sf{\cancel{\dfrac{24}{2}\:cm}}$

=$\sf{12\:cm}$

• Thickness of the cylinder is = 3 cm

.°. Internal radius of the cylinder is

$\sf{External\:radius\:of\:the\:cylinder- thickness\:of\:the\:cylinder}$

= $\sf{12-3\:cm}$

= $\sf{9\:cm}$

We know that,

$\boxed{\bf{\pink{Volume\:of\:cylinder=πr^{2}h}}}$

Where,

• r = radius of the cylinder
• h = height of the cylinder
• π = $\sf{\dfrac{22}{7}}$

$\sf{Volume\:of\:the\:external\:part\:of\:the\:cylinder\:is=πr^{2}h}$

= $\sf{\dfrac{22}{7}×12×168\:cm^{3}}$

= $\sf{22×12×24\:cm^{3}}$

= $\sf{6336\:cm^{3}}$

$\sf{Volume\:of\:the\:internal\:part\:of\:the\:cylinder\:is=πr^{2}h}$

= $\sf{\dfrac{22}{7}×9×168\:cm^{3}}$

= $\sf{22×9×24\:cm^{3}}$

= $\sf{4752\:cm^{3}}$

.°. The volume of metal used in making the cylinder is

$\sf{\implies (Volume\:of\:external\:part)-(Volume\:of\:internal\:part)}$

$\sf{\implies (6336-4752)\:cm^{3}}$

$\sf{\implies 1584\:cm^{3}}$

Now,

• given that, 1 cm³ metal = 15 g

.°. 1584 cm³ metal= 5 × 1584 cm³ = 23760 cm³

Therefore,

Volume of metal used in making the cylinder is 1584 cm³

⠀⠀

the weight of cylinder is 23760 If 2 cm cube of the metal weight 15 g.

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