A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is cast into a hollow cylindrical pipe of an internal radius of 30 cm and thickness of 5 cm. Find the length of the pipe?
Volumes are very important quantities that have many real-life applications. Starting from the gas cylinder in your homes to laboratory tests in hospitals, preciseness of volumes of substances is always kept in mind. Now let's solve a problem regarding volumes of cylinders and blocks.
Answer: The height of the hollow cylindrical pipe with an internal radius of 30 cm and thickness of 5 cm cast from the given solid block is 112 m.
Let's understand the solution in detail.
From the above information, the things known about the hollow cylinder are:
Internal radius, r = 30 cm
Thickness, t = 5 cm
Let the length of the pipe be h.
Therefore, the external radius, R is given by the sum of the internal radius and the thickness.
Hence, R = r + t = 30 + 5 = 35 cm.
Therefore, 440 × 260 ×100 = π (R2 – r2) h
After converting all quantities in meters:
440 × 260 × 100 = 22/7 (352 – 302) h
⇒ 440 × 260 × 100 = 22/7 (325) h
Hence, h = 11200 cm = 112 m