Question

# A metallic cylinder of diameter $$5\ cm$$ and height $$3\dfrac {1}{3}cm$$ is melted and cast into a sphere. What is its diameter?

A
5 cm
B
6 cm
C
7 cm
D
9 cm

Solution

## The correct option is A $$5\ cm$$Height of cylinder $$= 3 \dfrac{1}{3}$$ cm $$= \dfrac{10}{3}$$ cmDiameter of cylinder $$= 5$$ cm $$\therefore$$ Radius of cylinder $$= \dfrac{5}{2}$$ cm A metallic cylinder is melted and cast into a sphere $$\therefore$$ Volume of cylinder $$=$$ Volume of sphere                           $$\pi$$$$r^2$$h = $$\dfrac{4}{3}$$$$\pi$$$$r^3$$ $$\therefore$$ $$\pi$$ $$\times$$ $$\dfrac{5}{2}$$  $$\times$$ $$\dfrac{5}{2}$$ $$\times$$ $$\dfrac{10}{3}$$ $$=$$  $$\dfrac{4}{3}$$ $$\times$$$$\pi$$ $$r^3$$       $$\therefore$$ $$r^3$$ $$=$$ $$\dfrac{5\times5\times5}{2\times2\times2}$$$$\therefore$$ r $$=$$ $$\dfrac{5}{2}$$ cmDiameter $$=$$ radius $$\times$$ 2$$\therefore$$ Diameter = $$\dfrac{5}{2}$$ $$\times$$ 2$$\therefore$$ Diameter $$= 5$$ cm$$\therefore$$ Diameter of metallic sphere is $$5 cm.$$Mathematics

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