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  • How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

Answers (1)

Answer 1501

Solution

            It is given that the length, breadth and height of rectangular solid is 66cm, 42cm and 21cm respectively.

            Volume of solid rectangular lead piece = l \times b \times h

                        66 \times 42 \times 21

                        =5821 cm^3

            The diameter of spherical lead shot =4.2

            The radius of spherical lead shot

=\frac{4.2}{2}=2.1 cm

           \text{ The volume of lead shot }=\frac{4}{3}\pi r^3

                        =\frac{4}{3}\times 3.14 \times (2.1)^3=38.77 cm^3

        \text{ Number of lead shot can be obtained}=\frac{\text {volume of lead piece}}{\text{volume of lead shot}}

                        =\frac{58212}{38.77}=1501

            Hence 1501 lead shot can be obtained from the lead piece of dimensions 66cm, 42cm and 21cm

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