# A solid iron cuboidal block of dimensions 4.4m × 2.6m × 1m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find length of the pipe?

The volume is the space occupied by any solid shape.

## Answer: The length of the hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm is 11200cm or 112m

Let's find the length of the pipe.

**Explanation:**

Given: Dimesions of the cuboid is 4.4m × 2.6m ×1m

Length (L) = 4.4m

Breadth (B) = 2.6m

Height (H) = 1m

Let the inner radius of the hollow cylindrical pipe be 'r'

Thus, r = 30cm

Let the thickness of the hollow cylindrical pipe be 'x'

x = 5cm

Let length of the hollow cylindrical pipe be 'h'

Let the outer radius of the pipe be 'R'

Outer radius = Inner radius + thickness

Thus, R = r + x = 30 + 5 = 35cm

Since the cuboidal block is casted into a hollow cylinder, the volume will remain constant

Hence,

Volume of the cuboid = Volume of the hollow cylinder

=> L × B × H = π (R^{2}- r^{2}) h

=> 440 × 260 ×100 = (22/7) × (35^{2} - 30^{2}) × h

=> h = (440 × 260 ×100 × 7) / (22 × 325) (By transposing terms)

On solving,

=> h = 11200cm or 112m (since, 100cm = 1m)