Question

the thickness of a hollow metallic cylinder is 2 cm . It is 70 cm long with outer radiusof 14 cm . Find the volume of the metal used in making the cylinder ,assuming that it is open at both ends . Also find its weight if the metalbweights 8 g per cm^3​

Answer 1

Answer:

Let t is thickness of the cylinder

r

1

is outer radius of the cylinder

r

2

is inner radius of the cylinder

h is height of the cylinder

∴t=2cm

r

1

=14cm

h=70cm

Now, inner radius is calculated as,

r

2

=r

1

−t

∴r

2

=14−2=12cm

1) Volume of the hollow cylinder is given by,

V=c/sarea×heightofcylinder

∴V=(πr

1

2

−πr

2

2

)×h

∴V=π(14

2

−12

2

)×70

∴V=

7

22

(196−144)×70

∴V=22×52×10

∴V=11440cm

3

2) Given wright of the metal, ρ=8

cm

3

g

Let m = mass of the cylinder

∴ρ=

V

m

∴8=

11440

m

∴m=8×11440

∴m=91520gm

∴m=91.520kg

Answer 2

Answer:

Let t is thickness of the cylinder

r

1

is outer radius of the cylinder

r

2

is inner radius of the cylinder

h is height of the cylinder

∴t=2cm

r

1

=14cm

h=70cm

Now, inner radius is calculated as,

r

2

=r

1

−t

∴r

2

=14−2=12cm

1) Volume of the hollow cylinder is given by,

V=c/sarea×heightofcylinder

∴V=(πr

1

2

−πr

2

2

)×h

∴V=π(14

2

−12

2

)×70

∴V=

7

22

(196−144)×70

∴V=22×52×10

∴V=11440cm

3

2) Given wright of the metal, ρ=8

cm

3

g

Let m = mass of the cylinder

∴ρ=

V

m

∴8=

11440

m

∴m=8×11440

∴m=91520gm

∴m=91.520kg