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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
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B
6 cm
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C
7 cm
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D
9 cm
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Solution

The correct option is A $$5\ cm$$

Height of cylinder $$= 3 \dfrac{1}{3}$$ cm $$= \dfrac{10}{3}$$ cm

Diameter 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 $$=$$ $$\dfrac{5}{2}$$ cm

Diameter $$=$$ 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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