Question

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one.
How many such balls can be made


don't be greedy for points
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Answer 1

Given :

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one.

To find :

How many such balls can be made.

Solution :

Let the radius of big ball be 'r' cm

∴ Radius of smaller ball = r/2 cm.

➻ Volume of sphere = 4/3 πr³

Now volume of big spherical ball :

➻ Volume of big spherical ball = 4/3 πr³

Now volume of smaller spherical ball :

➻ Volume of smaller spherical ball = 4/3 π(r/2)³

Now number of balls can be made :

➻ Number of balls = Volume of big ball/Volume of smaller ball

➻ Number of balls = (4/3 πr³)/[4/3 π (r³/8)]

➻ Number of balls = (4/3 πr³)/[πr³/6]

➻ Number of balls = (4/3)/(1/6)       [Cancelling πr³]

➻ Number of balls = (4/3) × 6

➻ Number of balls = 4 × 2

➻ Number of balls = 8

∴ Number of balls can be made = 8

Answer 2

Answer:

Given :-

A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one.

To Find :-

Balls can be made

SoluTion :-

Let the radius of big circle be r

And radius of smaller circle is half so,

Radi of smaller circle = r/2

Now

We know that

Volume of bigger circle = 4/3πr³

Volume of smaller circle = 4/3 π (r/2)³

Now,

Let's find No. of balls

$\sf No. \: of \: balls = \dfrac{ \dfrac{4}{3}\pi \: r {}^{3} }{ \dfrac{4}{3}\pi \: \bigg( \dfrac{r}{2} \bigg) {}^{3} }$

$\sf \: No. \: of \: balls = \dfrac{ \frac{4}{3} \pi \: {r}^{3} }{ \frac{4}{3}\pi \: \frac{r {}^{3} }{8} }$

$\sf \: No. \: of \: balls = \frac{ \frac{4}{3} \times \pi \times r {}^{3} }{\pi \dfrac{r}^{3}{8}}$

$\sf \: No. \: of \: balls = \bigg( \dfrac{4}{3} \times 6 \bigg)$

$\sf \: No. \: of \: balls = 8$