A solid metal block in the form of a cuboid measures

MATHEMATICS · Multi-part · CBSE · Mathematics · Surface Areas and Volumes · Surface Areas and Volumes

Problem

A solid metal block in the form of a cuboid measures 32 cm×28 cm×12 cm32\text{ cm} \times 28\text{ cm} \times 12\text{ cm}. It is melted and cast into hollow cylindrical pipes, each of length 30 cm30\text{ cm}. For every pipe the external radius is 5 cm5\text{ cm} and the internal radius is 4 cm4\text{ cm}. (i) Determine the volume of metal in the cuboidal block. (ii) Calculate the volume of metal required to manufacture one pipe. (iii) Find the maximum number of complete pipes that can be made from the metal block.

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