Question

3. An iron ball of radius 21 cm is melted and recast into 27 spherical balls of the same radius. Find the radius of the each spherical ball.

Answer 1

AnswEr:

⋆ Reference of Image is shown in Diagram

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• It is given that 27 spherical balls are made from a sphere of 21 cm
• Here, Volume of Sphere(21cm) is equal to the 27 Spherical balls.

$\rule{170}2$

$\underline{\bigstar\:\textsf{According \: to \: the \: Question \: now:}}$

$\sf\ : \implies\ Volume_{big \: sphere} = 27 \times\ Volume_{spherical \: ball} \\\\\\\sf\ : \implies\frac{4}{3} \pi r^{3} = 27 \times\ \frac{4}{3} \pi r^{3}\\\\\\\sf\ : \implies\cancel{\frac{4}{3} \pi} (21)^{3} = 27 \times\ \cancel{\frac{4}{3} \pi} r^{3}\\\\\\\sf\ : \implies\ 9261 = 27 \times\ r^{3}\\\\\\\sf\ : \implies\ r^{3} = \frac{\cancel{9261}}{\cancel{27}} \\\\\\\sf\ : \implies\ r^{3} = 343\\\\\\\sf\ : \implies\ r = \sqrt[3]{343}\\\\\\\sf\ : \implies\ r = \sqrt[3]{ 7 \times\ 7 \times\ 7}\\\\\\ : \implies\boxed{\bf\green\ r = 7}\\\\\therefore{\textsf{Hence, the radius is \textbf{7cm}(each spherical ball)}}$