A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is melted

1.	A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
Answer» Let the length of the pipe be h cm. Then, Volume of cuboid = (53 x 40 x 15) cm³ Internal radius of the pipe = 7/2 cm = r External radius of the pipe = 8/2 = 4 cm = R So, the volume of iron in the pipe = (External Volume) – (Internal Volume) = πR²h – πr²h = πh(R²– r²) = πh(R – r) (R + r) = π(4 – 7/2) (4 + 7/2) x h = π(1/2) (15/2) x h Then from the question it’s understood that, The volume of iron in the pipe = volume of iron in cuboid π(1/2) (15/2) x h = 53 x 40 x 15 h = (53 x 40 x 15 x 7/22 x 2/15 x 2) cm h = 2698 cm Therefore, the length of the pipe is 2698 cm.

A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

Answer»

Let the length of the pipe be h cm.

Then, Volume of cuboid = (53 x 40 x 15) cm³

Internal radius of the pipe = 7/2 cm = r

External radius of the pipe = 8/2 = 4 cm = R

So, the volume of iron in the pipe = (External Volume) – (Internal Volume)

= πR²h – πr²h

= πh(R²– r²)

= πh(R – r) (R + r)

= π(4 – 7/2) (4 + 7/2) x h

= π(1/2) (15/2) x h

Then from the question it’s understood that,

The volume of iron in the pipe = volume of iron in cuboid

π(1/2) (15/2) x h = 53 x 40 x 15

h = (53 x 40 x 15 x 7/22 x 2/15 x 2) cm

h = 2698 cm

Therefore, the length of the pipe is 2698 cm.