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A solid piece of iron in the form of a cuboid of dimensions 49cm \times 33cm \times 24cm, is moulded to form a solid sphere. The radius of the sphere is

(A) 21cm                     (B) 23cm                     (C) 25cm                     (D) 19cm

Answers (1)

Answer (A) 21cm      


            Length of cuboid = 49 cm

            Breadth of cuboid = 33 cm

            Height of cuboid = 24 cm

            Volume =l \times b \times h

                        49 \times 33 \times 24=38808

            We know that volume of sphere \frac{4}{3}\pi r^{3}

            Also volume of sphere 38808  (given)

                        r^{3}=\frac{38808 \times 7 \times 3}{4 \times 22}=\frac{882 \times 7 \times 3}{2}=9261


                        r=\sqrt[3]{3 \times 3 \times 3 \times 7 \times7 \times 7}

                     r= 3 \times 7 = 21

            Hence radius of sphere = 21 cm

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