we know that
volume of a cone=(1/3)*pi*r²*h
clear variable h
volume=(1/3)*pi*r²*h-----> multiply by 3
3*volume=pi*r²*h----> divide by (pi*r²)
3*volume/(pi*r²)=h
h=3*volume/[pi*r²]
in this problem
volume=147*pi cm³
r=7 cm
so
h=3*[147*pi]/[pi*7²]-----> h=3*147/49----> h=9 cm
the answer is
the expression that can be used for calculate the height of the cone is
h=3*volume/[pi*r²]
the height of the cone is h=9 cm
