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

Solution:

Given, a solid iron cuboidal block is recast into a hollow cylindrical pipe.

Cuboidal block has dimensions 4.4 m × 2.6 m × 1 m

Hollow cylindrical pipe has an internal radius 30 cm and thickness 5 cm.

We have to find the length of the pipe.

Volume of cuboidal block = length × width × height

= 4.4 × 2.6 × 1

= 11.44 m³

Given, internal radius r = 30 cm

1 m = 100 m

So, r = 30/100 = 0.3 m

Thickness = 5 cm

External radius = internal radius + thickness

= 30 + 5

= 35 cm

So, R = 35/100 = 0.35 m

Volume of hollow cylinder = π(R² - r²)h

= (22/7)((0.35)² - (0.3)²)h

= (22/7)(0.0325)h

= 0.102h m³

Given, volume of cuboidal block = volume of pipe

11.44 = 0.102h

h = 11.44/0.102

h = 112.16 m

Therefore, the length of the pipe is 112.16 m.

✦ Try This: A solid iron cuboidal block of dimensions 3.3 m × 1.3 m × 0.8m is recast into a hollow cylindrical pipe of internal radius 20 cm and thickness 6 cm. Find the length of the pipe.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 9

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

Summary:

A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. The length of the pipe is 112.16 m

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