Question

Three spheres of radii 2cm, 3cm,4cm are melted together to form a single sphere.Find the radius of new sphere.

Answer 1

GIVEN :-

Radius of first sphere , $\sf r_1 = 2\ cm$

Radius of second sphere , $\sf r_2 = 3 \ cm$

Radius of third sphere , $\sf r_3 =4cm$

These three spheres are melted together to form a single sphere .

TO FIND :-

Radius of new sphere .

SOLUTION :- 

Volume of new sphere = Volume of first sphere + Volume of second sphere + Volume of third sphere.

Formula to find the volume of sphere = $\sf\dfrac{4}{3}\pi r^3$

Volume of first sphere ,       

$\longrightarrow\sf \dfrac{4}{3}\pi\times (r_1)^3\\\\\longrightarrow \dfrac{4}{3} \times \pi \times 2 \times2 \times2 \\\\\longrightarrow 33.5 \ cm^3$

Volume of second sphere ,        

 $\longrightarrow\sf \dfrac{4}{3} \pi \times (r_2)^3\\\\\longrightarrow \dfrac{4}{3} \times \pi \times 3 \times 3\times 3 \\\\\longrightarrow 113.04 \ cm^3$

Volume of third sphere , 

$\longrightarrow\sf \dfrac{4}{3}\pi \times (r_3)^3\\\\\longrightarrow \dfrac{4}{3} \times \pi \times 4 \times 4\times 4\\\\\longrightarrow 268 \ cm^3$ 

Volume of new sphere = 33.5 + 113.04 +

268                     

= 414.54 cm³    

 $\longrightarrow\sf \dfrac{4}{3} \times \pi \times r^3 = 414.54 \\\\\longrightarrow \dfrac{4}{3} r^3 = 132 \\\\\longrightarrow r^3 = 99\\\\\longrightarrow r=\sqrt[3]{99} \\\\\longrightarrow r = 4.626$

Radius of the new sphere = 4.626 cm

Answer 2

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