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  • Two spheres of same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere.    

Two spheres of same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere.

 

 
 
 
 
 

Answers (1)

Weight of smaller sphere = 1kg

weight of larger sphere = 7kg

Radius of smaller sphere (r) = 3cm

\begin{align*}\text{Volume of smaller sphere} & = \frac{4}{3}\pi r^3 \\ & = \frac{4}{3} \pi (3)^3 \\ & = 36\pi \ cm^3 \end{align*}

Density = \frac{weight}{volume} = \frac{w_1}{v_1} = \frac{w_2}{v_2}

            \Rightarrow \frac{w_1}{w_2} = \frac{v_1}{v_2}

Since 1kg metal sphere occupies = 36\pi\ cm^3

Weight of released metal sphere = (1 + 7) = 8kg

\begin{align*}\text{8kg sphere occupies} & = \frac{4}{3}\pi R^3 \\ 8\times 36\cancel{\pi}& = \frac{4}{3} \cancel{\pi} (R)^3 \\ R & = \sqrt[3]{6\times6\times 6}\\ R &= 6 cm\end{align*}

D = 2R = 12 cm

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Safeer PP

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