A solid cuboidal slab of iron of dimensions 66cm * 20cm * 27cm is used to cast an iron pipe. If the outer diameter of the pipe is 10cm and thickness is 1cm, then calculate the length of the pipe.

Given :The dimensions of iron slab are

Length (l) = 66 cm

Breadth (b) = 20 cm

Height (h) = 27 cm

we know that, Volume of iron slab()=l b h

so, V₁= 66 × 20 × 27= 35640 cm³...(1)

This slab is used to make iron pipe with outer diameter 10 cm and thickness 1 cm,

∴inner diameter =10-2cm=8cm

The outer radius (r₁) = 5 cm

inner radius (r₂) = 4 cm.

Letl₁be the length of the pipe (this will work as height of the cylindrical pipe)

∴ Volume of the pipe()= r²h

= 3.14 (5² 4²)l₁= 3.14 × (25 16)l₁

so,V₂= 3.14 × 9 ×l₁= 28.26 ×l₁cm³...(2)

Now, volume of iron slab and the pipe is same

Hence the length of pipe = 12.61 m

Given :The dimensions of iron slab are

Length (l) = 66 cm

Breadth (b) = 20 cm

Height (h) = 27 cm

we know that, Volume of iron slab()=l b h

so, V₁= 66 × 20 × 27= 35640 cm³...(1)

This slab is used to make iron pipe with outer diameter 10 cm and thickness 1 cm,

∴inner diameter =10-2cm=8cm

The outer radius (r₁) = 5 cm

inner radius (r₂) = 4 cm.

Letl₁be the length of the pipe (this will work as height of the cylindrical pipe)

∴ Volume of the pipe()= r²h

= 3.14 (5² 4²)l₁= 3.14 × (25 16)l₁

so,V₂= 3.14 × 9 ×l₁= 28.26 ×l₁cm³...(2)

Now, volume of iron slab and the pipe is same

Hence the length of pipe = 12.61 m