Given:
Height of a cone = 50 m
Volume of cone = 5400π
To find:
The radius of the cone
Solution:
Volume of cone:
[tex]$V=\frac{1}{3}\pi r^2h[/tex]
[tex]$\frac{1}{3}\pi r^2h=5400\pi[/tex]
Cancel common factor π on both sides.
[tex]$\frac{1}{3} r^2h=5400[/tex]
Substitute h = 50.
[tex]$\frac{1}{3}\times r^2\times 50=5400[/tex]
Multiply by 3 on both sides.
[tex]$3 \times \frac{1}{3}\times r^2\times 50=5400\times 3[/tex]
[tex]$ r^2\times 50=16200[/tex]
Divide by 50 on both sides, we get
[tex]r^2=324[/tex]
Taking square root on both sides, we get
[tex]r=18[/tex]
The radius of the cone is 18 m.
