Question

A metallic cylinder of diameter $5cm$ and height $3\frac{1}{3}cm$ is melted and cast into a sphere. What is its diameter?

• A. $5cm$
• B. $6cm$
• C. $7cm$
• D. $9cm$

Answer 1

The correct option is A $5cm$

Height of cylinder $=3\frac{1}{3}$ cm $=\frac{10}{3}$ cm

Diameter of cylinder $=5$ cm

$\therefore$ Radius of cylinder $=\frac{5}{2}$ cm

A metallic cylinder is melted and cast into a sphere

$\therefore$ Volume of cylinder $=$ Volume of sphere

$\pi$$r^2$h = $\frac{4}{3}$$\pi$$r^3$

$\therefore$ $\pi$ $\times$ $\frac{5}{2}$ $\times$ $\frac{5}{2}$ $\times$ $\frac{10}{3}$ $=$ $\frac{4}{3}$ $\times$$\pi$ $r^3$

$\therefore$ $r^3$ $=$ $\frac{5\times 5\times 5}{2\times 2\times 2}$

$\therefore$ r $=$ $\frac{5}{2}$ cm

Diameter $=$ radius $\times$ 2

$\therefore$ Diameter = $\frac{5}{2}$ $\times$ 2

$\therefore$ Diameter $=5$ cm

$\therefore$ Diameter of metallic sphere is $5cm.$