Question
A solid metal cone with base radius $12\ cm$ and height $24\ cm$ is melted to form solid spherical balls of diameter $6\ cm$ each. Find the number of balls formed.
✓
Answer
Radius of cone $= 12\ cm$
Height of cone $= 24\ cm$
Volume of the metallic cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi\times(12)^2\times24$
Radius of spherical ball $=\frac{6}{2}\text{cm}=3\text{cm}$
Volume of each spherical ball $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\pi\times(3)^3$
Number of balls formed $=\frac{\text{Volume of the metallic cone}}{\text{Volume of each spherical ball}}$
$=\frac{\pi\times12\times12\times24\times3}{3\times4\times\pi\times3\times3\times3}$
$=32$
Height of cone $= 24\ cm$
Volume of the metallic cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{1}{3}\pi\times(12)^2\times24$
Radius of spherical ball $=\frac{6}{2}\text{cm}=3\text{cm}$
Volume of each spherical ball $=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\pi\times(3)^3$
Number of balls formed $=\frac{\text{Volume of the metallic cone}}{\text{Volume of each spherical ball}}$
$=\frac{\pi\times12\times12\times24\times3}{3\times4\times\pi\times3\times3\times3}$
$=32$
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