A metal pipe is 70 cm in length. Its internal radius is 12mm and thickness is 1mm. If 1mm^3 of the metal weighs 0.05 gm, what is the weight of the pipe? Step by step explanation

Step-by-step explanation:

we have to calculate the volume of 2 pipes, actually.

the inner, empty volume of the pipe with radius of 12mm.

and the complete pipe volume including the pipe wall, which adds 1mm to the radius (12+1 = 13mm).

and then we need to subtract the volume of the inner, hole part from the general pipe volume.

and that is then the volume of the actual pipe material, which we will then "translate" to weight based on the given ratio of 1/0.05 mm³/gm

so, what is the volume of a pipe ? it is actually a cylinder. it has a circular base area, and the length is, of course, the height.

the area of a circle is pi×r².

and the cylinder volume is base area times height :

pi×r²×height

also to remember : 1cm = 10mm

so, length = height = 70×10 = 700mm.

it is always important to use the same dimension of numbers when combining them in a calculation.

Vi (inner volume) = pi×12²×700 mm³ = pi×144×700 mm³

Vt (total volume) = pi×13²×700 mm³ = pi×169×700 mm³

Vt- Vi = (169 - 144)×pi×700 = 25×pi×700 mm³ =

= 54,977.87144 mm³

now, to the weight.

1 mm³ weighs 0.05 gm.

but we have not 1 but 54,977.87144 mm³.

so, we need to multiply 0.05 by the amount of mm³ to get the total weight.

0.05×54,977.87144 = 2,748.893572 gm

the pipe weighs 2748.89 gm or 2.75 kg (1kg = 1000gm).