Question

A metal sphere 6cm in diameter is melted and cast into balls of diameter 0.5cm.How many of the smaller balls will there be?

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore No.\:of\:balls=1728}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a metal sphere 6cm in diameter is melted and cast into balls of diameter 0.5cm.

• We have to find no. of smaller balls .

$\underline \bold{Given : } \\ \implies Diameter \: of \: sphere = 6 \: cm \\ \\ \underline \bold{To \: find : } \\ \implies No. \: of \: balls \: of \: diameter \: 0.5 \: cm = ?$

• According to given question :

$\bold{Radius= \frac{6}{2} = 3 \: cm}\\ \\ \bold{Using \: formula\: volume \: of \: sphere : } \\ \implies Volum e\: of \: sphere = \frac{4}{3} \pi {r}^{3} \\ \\ \implies Volume_{1} = \frac{4}{3} \pi \: ({3})^{3} \\ \\ \implies Volume_{1} = 36\pi \: {cm}^{3} \\ \\ \bold{For \: Volume \: of \: small \: sphere : } \\ \implies Volume_{2} = \frac{4}{3} \pi \: ({ \frac{0.5}{2} })^{3} \\ \\ \implies Volume_{2} = \frac{4}{3} \pi \: \frac{0.125}{8} \\ \\ \implies Volume_{2} = \frac{0.125}{6} \pi \: {cm}^{2} \\ \\ \bold{For \: no. \: of \: balls : } \\ \implies No. \: of \: balls = \frac{Volume_{1}}{Volume_{2}} \\ \\ \implies No. \: of \: balls = \frac{36\pi}{ \frac{0.125}{6}\pi } \\ \\ \implies No. \: of \: balls = \frac{36 \times 6 \times \cancel\pi}{0.125 \times \cancel\pi} \\ \\ \bold{\implies No. \: of \: balls = 1728 \: balls}$

Answer 2

Step-by-step explanation:

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