Question
Three solid spheres of radii 3, 4 and 5cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
✓
Answer
Let R be the radius of single solid sphere.
Therefore,
Volume of single solid sphere = volume of all three spheres
$\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\pi\text{r}_1^3+\frac{4}{3}\pi\text{r}_2^3+\frac{4}{3}\pi\text{r}_3^3$
$\frac{4}{3}\pi\text{R}^3=\frac{4}{3}\pi(\text{r}_1^3+\text{r}_2^3+\text{r}_3^3)$
$\text{R}^3=(3^3+4^3+5^3)$
$\text{R}^3=27+64+125$
$\text{R}^3=216$
$\text{R}=\sqrt{216}$
$=6$
$\text{R}=6$
Therefore,
Volume of single solid sphere = volume of all three spheres
$\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\pi\text{r}_1^3+\frac{4}{3}\pi\text{r}_2^3+\frac{4}{3}\pi\text{r}_3^3$
$\frac{4}{3}\pi\text{R}^3=\frac{4}{3}\pi(\text{r}_1^3+\text{r}_2^3+\text{r}_3^3)$
$\text{R}^3=(3^3+4^3+5^3)$
$\text{R}^3=27+64+125$
$\text{R}^3=216$
$\text{R}=\sqrt{216}$
$=6$
$\text{R}=6$
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