from a handpicked tutor in LIVE 1-to-1 classes

# 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 11200 cm or 112 m.

Let's find the length of the pipe.

**Explanation:**

Given: Dimensions of the cuboid is 4.4 m × 2.6 m ×1 m.

Length (L) = 4.4 m = 440 cm

Breadth (B) = 2.6 m = 260 cm

Height (H) = 1 m = 100 cm

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

Thus, r = 30 cm

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

⇒ x = 5 cm

Let, the length of the hollow cylindrical pipe be 'h' cm.

Let the outer radius of the pipe be 'R' cm.

Outer radius = Inner radius + thickness

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

Since the cuboidal block is cast 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 = 11200 cm or 112 m (since, 100 cm = 1 m)

### Thus, the length of the hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm is 11200 cm or 112 m.

visual curriculum