Question

How many balls,each of radius 1 cm,can be made from a solid sphere of lead of radius 8cm?​

Answer 1

Answer:-

Required number of balls = $\bf{512}$

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• Solution:-

Volume of the spherical ball of radius 8cm

$\\ =\frac{4}{3}\pi \times 8^{3} \: cm^{3}$

Also, volume of each smaller spherical ball of radius 1 cm

$\\ =\frac{4}{3\pi \times 1^{3}} \: cm^{3}$

Let $\bf{n}$ be the number of smaller balls that can be made.Then, the volume of the larger ball is equal to the sum of all the volumes of $\bf{n}$ smaller balls.

Hence,

$\large{\frac{4}{3}}\pi \times n$=$\large{\frac{4}{3}}\pi \times 8^{3}$

$\implies \large{n= 8^{3} = 512}$

Hence, the required number of balls is $\bf{512}$

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