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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.

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.

Answers (1)

Answer 112m

Solution

            Length of cuboidal block = 4.4m

            Breadth = 2.6 m

            Height = 1 m

            Volume =l \times b \times h

                         = 4.4 \times 2.6 \times 1

                        = 4.4 \times 2.6 \times m^3

            Radius of cylindrical pipe r1 = 30cm = 0.3m

                        r2 = 30+5 = 35cm = 0.35 m

                        Let, Height h1

            Volume =\pi r ^2 h

                        =\frac{22}{7}\times h_{1} \left ( (0.35)^2-(0.3)^2 \right )             

            The volume of cuboid = volume of the cylindrical pipe

                        =4.4 \times 2.6\times \frac{22}{7}\times h_{1}\left [ \left ( \frac{35}{100} \right )^2 -\left ( \frac{30}{100} \right )^2 \right ]

                        =\frac{44}{10} \times \frac{26}{10}\times \frac{22}{7}\times h_{1}\left [\frac{(35-30) (35+30)}{(100)^2} \right ] \left (a^2-b^2)=(a-b)(a+b) \right )

                        h_{1}=\frac{44}{10} \times \frac{26}{10}\times \frac{7}{22}\times \frac{100 \times 100}{5 \times 65}

                       h_{1}=112m

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