Question

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire. [4 MARKS]

Answer 1

Formula Framing: 2 Marks
Application: 1 Mark
Solution: 1 Mark

Let the radius of sphere be r cm
Let radius and length of wire be R and h respectively
$\begin{array}{ccc}Accordingtoquestion& Volumeofsphere=Volumeofwire\Rightarrow & \frac{4}{3}\pi r^3=\pi R^{2}h\\ \Rightarrow & \frac{4}{3}\times (3{)}^3=0.1\times 0.1\times h& \\ \Rightarrow & h=\frac{4\times (3{)}^2}{0.1\times 0.1}& \\ \Rightarrow & h=3600cm=36m& \end{array}$
$\therefore$ Length of wire = 36 m