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  • Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is (A) 4 cm

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

(A) 4 cm                      (B) 3 cm                      (C) 2 cm                      (D) 6 cm

Answers (1)

Answer(C) 2 cm

Solution

            Diameter of metallic cylinder = 2 cm

            Radius =\frac{2}{2}=1cm

            Height = 16cm

            Volume =\pi r^{2}h

                        =\pi\times 1 \times 1 \times 16= 16\pi

            We know that twelve solid sphere are made by melting of solid metallic cylinder

            Volume of sphere =\frac{4}{3}\pi r^{3}

            Hence volume of 12 spheres =16 \pi

                        =12 \times \frac{4}{3}\pi r^{3}=16 \pi

                        =16\pi r^{3}=16 \pi

                        r^{3}=1

                        r=1

            Radius = 1 cm

            Diameter 2 \times 1 = 2cm

Posted by

infoexpert21

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