Question

Metallic spheres of radii 6cm, 8cm and 10cm respectively are melted to form a

solid sphere. Find the radius of the resulting sphere.

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Answer 1

Answer:

metallic spheres of raddi 6cm, 8cm, and 10cm

if they are melted and they formed into a single sphere then all the raddibof sphere gets added

∴new raddi of sphere = 6+8+10=24

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Answer 2

Step-by-step explanation:

Radius of 1st sphere (r₁) = 6cm

Radius of 2nd sphere (r₂) = 8cm

Radius of 3rd sphere (r₃) = 10cm

Let the radius of the resulting sphere be " r "

Volume of 1st sphere = $\dfrac{4}{3} \pi (r_{1})^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: = \dfrac{4}{3} \pi \times 6^{3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{4}{3} \pi \times 216$

Volume of 2nd sphere = $\dfrac{4}{3} \pi (r_{2})^{2}$

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

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{4}{3} \pi \times 512$

Volume of 3rd sphere = $\dfrac{4}{3} \pi (r_{3})^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{4}{3} \pi \times 10^{3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: = \dfrac{4}{3} \pi \times 1000$

Volume of resulting sphere = Sum of volumes of the three spheres

$\rm \dashrightarrow \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3} \pi \times 216 + \dfrac{4}{3} \pi \times 512 + \dfrac{4}{3} \pi \times 1000$

$\rm\dashrightarrow \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\pi \big( 216 + 512 + 1000\big)$

$\dashrightarrow r^{3} = 216 + 512 + 1000$

$\dashrightarrow r^{3} = 1728$

$\dashrightarrow r= \sqrt[3]{1728}$

$\dashrightarrow r= 12cm$

$\underline{\boxed{\rm \therefore Radius \: of \: the \: resulting \: sphere = 12cm}}$