Question

how many solid balls each of radius 2cm can be made by melting a solid sphere of lead of radius 10 cm​

Answer 1

Given:

• Radius of each solid ball, r = 2 cm
• Radius of solid sphere, R = 10 cm

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To find:

• No. of solid balls?

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Solution:

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☯ Let number of balls be n.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• Solid balls are melted to form a solid sphere of lead.

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Therefore,

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★ Number of balls × Volume of 1 ball = Volume of solid sphere

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$:\implies\sf n \times \bigg( \dfrac{4}{3} \times \pi \times (2)^3 \bigg) = \dfrac{4}{3} \times \pi \times (10)^3$

$:\implies\sf n \times \cancel{\dfrac{4}{3}} \times \cancel{\pi} \times 8 = \cancel{\dfrac{4}{3}} \times \cancel{\pi} \times 1000$

$:\implies\sf n \times 8 = 1000$

$:\implies\sf n = \cancel{\dfrac{1000}{8}}$

$:\implies{\boxed{\sf{\purple{n = 125}}}}\;\bigstar$

$\therefore\;{\underline{\bf{Hence,\;125\;balls\;are\;melted\;to\;form\;a\;solid\;sphere.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• Total surface area of sphere = 4πr²

• Volume of sphere = $\bf \dfrac{4}{3} \pi r^3$

• Curved surface area of hemisphere = 2πr²

• Total surface area of hemisphere = 3πr²

• Volume of hemisphere = $\bf \dfrac{2}{3} \pi r^3$

Answer 2

Answer:

Given:

Radius of each solid ball, r = 2 cm

Radius of solid sphere, R = 10 cm

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To find:

No. of solid balls?

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Solution:

☯ Let number of balls be n.

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$\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}$

Solid balls are melted to form a solid sphere of lead.

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Therefore,

★ Number of balls × Volume of 1 ball = Volume of solid sphere

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$\begin{gathered}:\implies\sf n \times \bigg( \dfrac{4}{3} \times \pi \times (2)^3 \bigg) = \dfrac{4}{3} \times \pi \times (10)^3\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf n \times \cancel{\dfrac{4}{3}} \times \cancel{\pi} \times 8 = \cancel{\dfrac{4}{3}} \times \cancel{\pi} \times 1000\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf n \times 8 = 1000\\ \\\end{gathered}$$\begin{gathered}:\implies\sf n = \cancel{\dfrac{1000}{8}}\\ \\\end{gathered}$

$.\begin{gathered}:\implies{\boxed{\sf{\purple{n = 125}}}}\;\bigstar\\ \\\end{gathered}$

$\therefore\;{\underline{\bf{Hence,\;125\;balls\;are\;melted\;to\;form\;a\;solid\;sphere.}}}$

Step-by-step explanation:

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