Question

A spherical shell of lead whose external radius is 9 cm is melted and recast into a right circular cylinder 8 cm high and 12 cm in diameter. Find the diameter of the shell. [4 MARKS]

Answer 1

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

External radius of shell, R = 9 cm
Radius of cylinder $r_1=6cm$ Height of cylinder, h = 8 cm
According to question, Volume of spherical shell of lead = Volume of cylinder
$\begin{array}{cc}\Rightarrow & \frac{4}{3}\pi (R^3-r^3)=\pi r_1^{2}h\\ \Rightarrow & \frac{4}{3}\times (9^3-r^3)=6\times 6\times 8\\ \Rightarrow & 729-r^3=216\\ \Rightarrow & 729-216=r^3\\ \Rightarrow & r^3=513\\ \Rightarrow & r=\sqrt[3]{3513}\\ \Rightarrow & r=8cm(approx.)\end{array}$
$\therefore$ Inner diameter of the shell=2r=16cm (approx.)